Relationship between Age, Gender and Health Status - Research Paper Example

Running Head: Health, Age and Gender Health, Age and Gender Table of Contents Table of Contents 2 Introduction 3 Theoretical Framework 3 Data 5 Population Data 5 Sample 5 Analysis: 6 Gender 6 Health Status 7 Age 8 Health Status and Gender 9 Econometric Model 11 Simple Regression 11 Functional Form 12 Test of Normality of Residuals 14 Constructing Jarque-Bera test 16 Box Cox Test 18 Ramsey Regression Specification Error Test 19 Multicollinearity 19 Conclusion 29 References 29 Appendixes 30 Introduction This paper focuses on health status as related to age and gender, trends in health status as related to age and gender can be associated with social economic status and biological factors. The following is a discussion of the theories that relate to health, age and gender, the discussion shows that women get ill often than men, also that older individuals get ill often than younger age groups. Using data from the Wales health survey website data regarding health status, age and sex is retrieved in order to estimate a model that shows the relationship between health, age and gender. Theoretical Framework According to Doyle (1995) there is a difference in life expectancy and health status among men and women, in this study he states that men are more likely to die while women are more likely to get ill often, also that women life expectancy was higher than that of men, this means that health status differs between male and female whereby women often get ill but higher life expectancy than men. The difference in health status between male and female is partially explained by the difference in life expectancy, women are more likely to live longer and given that older people get ill often then the majority of individuals who fall ill are women, he points out that women fall ill due to biological factors, these biological factors include the fact that men have greater resistance to diseases than women, the other factor is that women are more likely to report illnesses unlike men. (Steve, 2007). The difference in health status between men and women is also explained by social economic factors, this include the concept that women are more likely to be poor or have lower levels of income and therefore may fall ill often. The other reason is that women live in a male dominated world and therefore are more likely to be depressed, face domestic violence and other incidences. Men on the other hand are more likely to engage in risky activities such as smoking and drinking and for this reason their life expectancy is lower than that of women. (Doyle, 1995). With reference to age health status differs across age groups, the population structure is influenced by social economic factors, the dependency ratio which refers to the proportion of the elderly and the labour force is an important measure in the modern society, the old in the society are more likely to have lower income levels than younger individuals, due to this differences then older people are more likely to fall ill often, the other reason is that women comprise of the majority of these old individuals in the society and therefore are more likely to fall ill often. (Steve, 2007). The other reason why older individuals fall ill often is due to social change that have changed the attitude toward the older individuals, in the modern society due to technological changes older people are not revered due to their experience, they are seen as a burden to the economy because they are unproductive. Differences in health status between the age groups can also be explained by factors such as exercises whereby younger age groups exercise more than older age groups, the other reason is biological factors whereby older people have less resistance to diseases and therefore are more likely to fall ill often. (Steve, 2007). Data Population Data Data was retrieved from Wales health survey website and is available at wales.gov.uk/docs/statistics/2009/090929hlthsurvey08ch3en.xls, data contains information regarding health status, age and sex, the health variable has five categories and they include excellent, very good, good, fair and poor health status, these categories are assigned number 1 to 5 respectively, therefore this means that the higher the value of health status then the individuals has poor health status. Age is also has seven age groups and they include those aged 16-44 years, 25-34,45-64 and 65+ years, these age groups are assigned number 1 to 3 respectively whereby a higher age value shows than an individual is older. Finally gender is treated as a dummy variable whereby the value 1 shows that the individual is male and number 0 means the individual is female. Sample The population size N = 13226 and therefore we selected a sample that will represent the entire population; an appropriate sample size is calculated as follows: n = N / (1+N (e2)). Where n is the sample size, N is the population size and e is the expected error which in this case is 5%, the following is a summary of these calculations: n = 13226 / (1+13226 (0.052)) therefore n = 388.258 and the sample size is assumed to be 400. A stratified sample is selected which represent all the age groups, sex and health status, from the results there data set is selected and using STATA the following are the results: Analysis: Gender Given that the population male and female number is almost equal the sample selected contains 200 male and 200 female respondents, given that 1 represents male and 0 represents female and that 1 depicts excellent health status and 5 poor health status then the following table summarizes the relationship between gender and health: health gender 1 2 3 4 5 0 28 65 60 35 12 1 32 66 58 29 15 From the table there are more male than female with excellent health status, however there are male than female with poor health status. The above frequency values are summarised in the following bar charts The chart above summarises health status of male respondents: The chart above summarises health status of male respondents: From the two charts there are more female participants with health status value of 2 and 3 compared to male health status chart. Health Status Health status is another variable in the data; this variable shows the health status of the respondents, from the table below majority of the individuals have good health status with only 27 individuals with poor health status, the table below summarizes the results: health Freq. 1 60 2 131 3 118 4 64 5 27 The chart below summaries the percentage number of Individuals classified with reference to health status; From the chart 32.7% respondents had good health status, only 6.75% respondents had poor health status and only 15% had excellent health status. Age Age groups was also another variable in the data, the value 1 represented those aged 16 – 44, 2 represented those aged between 45 – 64 and 3 represented those aged 65 and above. The table below summarizes the results: age Freq. 1 155 2 140 3 105 From the table majority of the individuals were aged 16 to 44 years while only 105 were aged 65 years and above, this means that majority of the respondents were young while only a few were older. The chart below summarizes the results: The chart shows that 38.75% of the respondents were aged 16 to 44 years, 35% were aged 45 to 64 years and 26.25% were aged 65 years and above. Health Status and Gender The relationship between health and age can be analyzed using a scatter diagram; the diagram below shows the relationship between the two variables: From the chart as the age scale increases then the health value also increases, from the health scale as the health status value increases then this means that health is deteriorating whereby value 1 means that an individual has excellent health while value 5 shows that an individual has poor health. Descriptive Statistics N Minimum Maximum Mean Std. Error Std. Deviation Statistic GENDER 400 1 2 1.5 0.025031 0.500626174 HEALTH 400 1 5 2.6675 0.055903 1.118064811 AGE 400 1 3 1.875 0.039874 0.797474083 Valid N 400           The mean gender is 1.5 (±.025) with a standard deviation of .5 while the mean of health is 2.67(±.056) and standard deviation of 1.12. The mean of age is 1.875(±.039) with a standard deviation of .79. This means that the amount of variations in the health status in large than in gender and age. Autocorrelation Please note that the time variable; i.e. age is repetitive and does not permit for Breusch-Godfrey Test to be carried out. Econometric Model Simple Regression In this section the simple regression models are estimated to show the relationship between health, age and gender, using the above theories the models are specified as follows: Health Status and Gender The model is specified as follows: Health status = a1 + b1 gender + Ei The value of b1 is expected to be negative given that the value of gender 1 means that the respondent is male, male individuals will yield a lower level of health status as stated in the theoretical framework whereby women are more likely to get ill often than men. The value of a1 is expected to be positive given that health status should be positive even when the value of gender is zero. Results The table below summarizes the results: Number of obs = 400 F( 1, 398) = 0.16 Prob > F = 0.687 R-squared = 0.0004 Adj R-squared = -0.002 health Coef. Std. Err. t P>t [95% Conf. Interval gender -.045 .1119241 -0.40 0.688 -.2650364 .175036 _cons 2.69 .0791423 33.99 0.000 2.534411 2.84558 From the above results the estimated model is as follows: Health status = 2.69 -0.045 gender. The model states that when gender = 1(male) then the value of health status declines by -0.045(move toward the value 1 which is excellent health status), if the gender value is zero (female = 0) then the health status value is 2.69. The value of R2 = .0004 means that the total variation in health status which is explained by gender is about (.0004*100) = .04. This is a very small variation and means that gender has very little to do with the variations in health status. This assertion is further insinuated by the p-value (.688) of the gender coefficient. The constant is a significant at 95% level of significance. Functional Form The basic idea behind testing for the appropriate functional form of the dependent variable is to transform the data so as to make the RSS comparable. Variable | Type Obs Mean [95% Conf. Interval] -------------+---------------------------------------------------------- gender | Arithmetic 400 1.5 1.45079 1.54921 | Geometric 400 1.414214 1.366789 1.463284 | Harmonic 400 1.333333 1.290981 1.378559 -------------+---------------------------------------------------------- health | Arithmetic 400 2.6675 2.557598 2.777402 | Geometric 400 2.414617 2.306019 2.528328 | Harmonic 400 2.147843 2.041615 2.265733 -------------+---------------------------------------------------------- age | Arithmetic 400 1.875 1.796611 1.953389 | Geometric 400 1.70061 1.626841 1.777725 | Harmonic 400 1.538462 1.474653 1.608042 ------------------------------------------------------------------------ The geometric mean of the health status is 2.41 and thus the regression of the log of dependent variable yields F > Computed (p = 0.000). The null hypothesis rejected and the alternative accepted. Source | SS df MS Number of obs = 400 -------------+------------------------------ F( 1, 398) = . Model | 498.355 1 498.355 Prob > F = 0.0000 Residual | .422500263 398 .001061558 R-squared = 0.9992 -------------+------------------------------ Adj R-squared = 0.9992 Total | 498.7775 399 1.25006892 Root MSE = .03258 99% of the explained variability in health status is explained using the residual analysis. Test of Normality of Residuals A normal distribution is symmetric about its mean (in this case zero). A Non-symmetric distribution is said to be skewed. One can measure this by looking at the 3rd moment of the normal distribution relative to the 2nd. Right skewness gives a value > 0 (more values clustered to close to left of mean and a few values a long way to the right of the mean tend to make the value >0). Left skewness gives a value < 0. In this case, plotting the residuals of the model with health status and age yields the figure below; From the figure it is evident that the residuals are skewed towards the left and is platykurtic in nature. The details of the residuals are as provided below; Percentiles Smallest 1% -1.117066 -1.148849 5% -1.074688 -1.148849 10% -1.03231 -1.12766 Obs 400 25% -.9581489 -1.12766 Sum of Wgt. 400   50% -.0217157 Mean -7.50e-10 Largest Std. Dev. .7800738 75% .0418511 1.978284 90% 1.00477 1.988879 Variance .6085152 95% 1.041851 2.010068 Skewness .4422028 99% 1.972987 2.031257 Kurtosis 2.830119 Constructing Jarque-Bera test JB = (400/6)*((.4422^2)+(((2.83-3)^2)/4)) =13.51 The statistic has a Chi2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). From tables critical value at 5% level for 2 degrees of freedom is 5.99 So JB >χ2 critical, so the null hypothesis that residuals are normally distributed is rejected. In the case of the gender and the health status, the normality plot is; The residual details are as follows; Percentiles Smallest 1% -.5438769 -.5438769 5% -.5438769 -.5438769 10% -.5303385 -.5438769 Obs 400 25% -.5303385 -.5438769 Sum of Wgt. 400 50% .4561231 Mean 3.73e-10 Largest Std. Dev. .4996122 75% .4696615 .4967385 90% .4832 .4967385 Variance .2496123 95% .4832 .4967385 Skewness -.1194802 99% .4967385 .4967385 Kurtosis 1.016093 Constructing Jarque-Bera test JB = (400/6)*((-.119^2) + (((1.016-3)^2)/4)) =64.66 The statistic has a Chi2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). From tables critical value at 5% level for 2 degrees of freedom is 5.99 So JB >χ2 critical, so the null hypothesis that residuals are normally distributed is rejected. Box Cox Test Number of obs = 400 LR chi2(0) = 0.00 Log likelihood = -287.77494 Prob > chi2 = . ------------------------------------------------------------------------------ Gender | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /theta | .5204958 .250695 2.08 0.038 .0291426 1.011849 ------------------------------------------------------------------------------ The Box Cox test for the gender shows its significance to health status (p = .038) Number of obs = 400 LR chi2(0) = 0.00 Log likelihood = -1164.4287 Prob > chi2 = . ------------------------------------------------------------------------------ age | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /theta | -.8273071 .3489457 -2.37 0.018 -1.511228 -.143386 ------------------------------------------------------------------------------ The Box Cox test for age in relation to health status also shows that age is significant (p = .018) Ramsey Regression Specification Error Test Ramsey RESET test using powers of the fitted values of health status yields the below results Ho: model has no omitted variables F (3, 395) = 1.48 Prob > F = 0.2181 From the results, specification error is not likely to be related the functional form of the variables currently in the model. Multicollinearity It is another common regression problem is all about the inclusion of highly correlated independent variables in a single regression model. To test for Multicollinearity between health status and gender; Collinearity Diagnostics SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- Health Status 1.00 1.00 0.9996 0.0004 Gender 1.00 1.00 0.9996 0.0004 ---------------------------------------------------- Mean VIF 1.00 Cond Eigenval Index --------------------------------- 1 2.8459 1.0000 2 0.1166 4.9406 3 0.0375 8.7133 --------------------------------- Condition Number 8.7133 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.9996 The two variables i.e. health status and gender are not highly correlated since R squared is small (.0004) For health status and age, the results indicate that; Collinearity Diagnostics SQRT Variable VIF VIF Tolerance R Squared ---------------------------------------------------- Health Status y 1.00 1.00 0.9961 0.0039 Age 1.00 1.00 0.9961 0.0039 ---------------------------------------------------- Mean VIF 1.00 Cond Eigenval Index --------------------------------- 1 2.8977 1.0000 2 0.0904 5.6616 3 0.0119 15.6341 --------------------------------- Condition Number 15.6341 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.9961 Health status and age are not highly correlated. Endogenity This all about the significance of the regression equation coefficients; To test for the coefficient of gender, Gender = 0 F( 1, 398) = 0.34 Prob > F = 0.5617 We accept the null that that the coefficient of gender is 0. Source | SS df MS Number of obs = 400 -------------+------------------------------ F( 1, 398) = 0.34 Model | .4225 1 .4225 Prob > F = 0.5617 Residual | 498.355 398 1.25214824 R-squared = 0.0008 -------------+------------------------------ Adj R-squared = -0.0017 Total | 498.7775 399 1.25006892 Root MSE = 1.119 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .065 .1118994 0.58 0.562 -.1549878 .2849878 _cons | 2.57 .1769285 14.53 0.000 2.222169 2.917831 Running regression for the residuals; Source | SS df MS Number of obs = 400 -------------+------------------------------ F( 2, 397) = . Model | 498.7775 2 249.38875 Prob > F = . Residual | 0 397 0 R-squared = 1.0000 -------------+------------------------------ Adj R-squared = 1.0000 Total | 498.7775 399 1.25006892 Root MSE = 0 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .065 . . . . . res2 | 1 . . . . . _cons | 2.57 . . . . . ------------------------------------------------------------------------------ The coefficients are the same which except on the measurement errors which are different from the top model. This means that the model cannot survive without gender. Testing for the coefficient of age then, Age = 0 F ( 1, 398) = 1.56 Prob > F = 0.2122 The null hypothesis is accepted that the coefficient of age is 0 Source | SS df MS Number of obs = 400 -------------+------------------------------ F( 1, 398) = 0.22 Model | .276416256 1 .276416256 Prob > F = 0.6388 Residual | 498.501084 398 1.25251529 R-squared = 0.0006 -------------+------------------------------ Adj R-squared = -0.0020 Total | 498.7775 399 1.25006892 Root MSE = 1.1192 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0330049 .0702568 0.47 0.639 -.1051159 .1711258 _cons | 2.605616 .143124 18.21 0.000 2.324242 2.886989 Running regression for the residuals; Source | SS df MS Number of obs = 400 -------------+------------------------------ F( 2, 397) = . Model | 498.7775 2 249.38875 Prob > F = . Residual | 0 397 0 R-squared = 1.0000 -------------+------------------------------ Adj R-squared = 1.0000 Total | 498.7775 399 1.25006892 Root MSE = 0 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0330049 . . . . . res3 | 1 . . . . . _cons | 2.605616 . . . . . ------------------------------------------------------------------------------ The coefficients are the same which except on the measurement errors which are different from the top model. This means that the model cannot survive without gender. Hypothesis Test Gender coefficient: Null hypothesis: B1 = 0, alternative hypothesis B1 ≠ 0 Given that the T statistics value < T critical value, then the null hypothesis is accepted, this means the gender coefficient is not statistically significant Constant value: Null hypothesis: a1 = 0, alternative hypothesis a1 ≠ 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the constant is statistically significant Health status and age: The model is specified as follows: Health status = a2 + b2 age + Ei The value of b2 is expected to be positive given that as age increases health status also increases, the value of a2 is expected to be positive given that health status should be positive even when the value of age is zero. Results: The table below summarizes the results: Number of obs = 140 F( 1, 1403) = 258.05 Model 266.062098 1 266.062098 Prob > F = 0.0000 Residual 1446.53861 1403 1.03103251 R-squared = 0.1554 Adj R-squared = 0.1548 Total 1712.60071 1404 1.21980108 Root MSE = 1.0154 Health status Coef. Std. Err. t P>t [95% Conf. Interval] age .2170625 .0135123 16.06 0.000 .190556 .243569 _cons 1.770863 .0603805 29.33 0.000 1.652417 1.889309 From the table the model is specified as follows Health status = 1.770863 + 0.217 age The above model states that as age increases then health status increases, an increase in the value of health status means that an individual will move from excellent health status to poor health status, the R squared value of the model is 0.1554 meaning that 15.54% deviations in health status is explained by age. The value of the residuals due to the variables is 1446.53 while that for the whole model is 1712.6. The coefficient of age is statistically significant at 95% level of significance while the constant is also significant. The residuals plot is as show above. The predicted health status goes up with gender and females have a higher score than males. Hypothesis test: Age coefficient: Null hypothesis: B2 = 0, alternative hypothesis B2 ≠ 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the age coefficient is statistically significant Constant value: Null hypothesis: a1 = 0, alternative hypothesis a1 ≠ 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the constant is statistically significant Multiple regressions: This section estimates a multiple regression model where age and gender are independent variables and health status is the dependent variable; Model specification; Models are specified with reference to existing theories, using our discussion on theories that depict the relationship between health, age and gender the model is specified as follows: Health status = a1 + b1age + b2 gender Expected signs: We expect that the value of b1 will be positive, this will mean that as age increases then health status increases from excellent to poor, the value of b2 is expected to negative and this means that when the value of gender is one which means the respondent is male then health status is expected to have a lower value (health scale: 1 excellent and 5 poor) Results: The table below summarizes the results: Number of obs = 400 F( 2, 397) = 28.25 Prob > F = 0.0000 R-squared = 0.1246 Adj R-squared = 0.1202 health Coef. Std. Err. t P>t [95% Conf. Interval] gender -.045 .1048723 -0.43 0.668 -.2511745 .1611745 age .4940887 .0658351 7.50 0.000 .3646596 .6235178 _cons 1.763584 .1440026 12.25 0.000 1.480481 2.046687 From the table the model can be stated as follows: Health status = a1 + 0.4940887age -0.045gender The above model states that when gender is male then health status declines, also when the age value is increased the health status increases. Hypothesis test: Age coefficient: Null hypothesis: B1 = 0, alternative hypothesis B1 ≠ 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the age coefficient is statistically significant Gender coefficient: Null hypothesis: B2 = 0, alternative hypothesis B2 ≠ 0 Given that the T statistics value < T critical value, then the null hypothesis is accepted, this means the gender coefficient is not statistically significant Constant value: Null hypothesis: a1 = 0, alternative hypothesis a1 ≠ 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the constant is statistically significant F test: Null hypothesis: a1 =b1=b2 = 0, alternative hypothesis a1 ≠ b1 ≠ b2 ≠ 0 Given that the F statistics value > F critical value, then the null hypothesis is rejected; this means the coefficients are statistically significant. Chow test; Given that we have male and female we test whether the two group coefficients are equal, this entails determining whether the age coefficient estimated using male only data is equal to the coefficient estimated using female only data: The estimated model is as follows: Health = b1 age + Ei The above model is split into two models: Health1 = a1 + b1 age1 + Ei (male group data) Health2 = a1 + b2 age2 + Eii (female group data) The two equations are then combined as follows: H = D1 ( b1 age1 + Ei) + D2(b2 age2 + Eii) Where D1 = 1 when considering male and zero for the female group data, D2 i=1 when considering female data and zero when considering male data. Therefore: H = D1b1age1 + D1Ei + D2b2age2 + D2Eii And: H = b1(D1age1) + b2(D2age2+ D1Ei+ D2Eii This is the model to be estimated, two groups are formed which is group 1 and group 2, group 1 contain data where respondents are male and group 2 contains data whose gender is female, also new variables are generated whereby age1 = age * group1 and age 2 = age* group 2. The following table summarises the estimated of the above model: Number of obs = 400 F( 2, 398) = 871.01 Prob > F = 0.0000 R-squared = 0.8140 Adj R-squared = 0.8131 health Coef. Std. Err. t P>t [95% Conf. Interval] age1 1.273824 .0434223 29.34 0.000 1.188458 1.35919 age2 1.287605 .04337 29.69 0.000 1.202342 1.372868 The estimated model is stated as follows: H = 1.273824D1age1 + 1.287605D2age2 We now test whether b1 = b2 = 0 using STATA, the following table shows the results: . test age1=age2 ( 1) age1 - age2 =0 F( 1, 398)= 0.05 Prob > F =0.8224 From the F test the null hypothesis that the two coefficients are equal is accepted, this means that the coefficient is equal for both male and female participants. This means that the impact of age on health status for both male and female is relatively equal. Heteroskedasticity: One assumptions of the linear regression model is that the variance of the error term is constant across observations, when this assumption is violated then we have Heteroskedasticity. Consequences are that the estimated coefficients are biased and the estimated values of standard errors are biased. The following table summarises results for the Breusch Pagan test for Heteroskedasticity Breusch-Pagan / Cook-Weisberg test for Heteroskedasticity Ho: Constant variance Variables: fitted values of health chi2(1) = 1.33 Prob > chi2 = 0.2480 The null hypothesis that the variance is constant is accepted and therefore the error term has a constant variance. Conclusion Theories have been developed to explain the relationship between age and health status, health and gender, from these theories some argue that women are more likely to get ill than mean, analyzing the relationship between gender and health status show that male are more likely to have better health status than women. Age is also a factor that influence health status, as individuals grow old their health status deteriorates and this is depicted by the regression showing the relationship between age and health where as age increases the health status shifts to poor health status. The Chow test on the equality of the age coefficient for both female and male groups shows that the coefficients are equal, the null hypothesis that the two coefficients are equal is accepted, and this means that the coefficients are equal for both male and female participants. This means that the impact of age on health status for both male and female is relatively equal. Other studies should aim at determine other factors that influence the health of individuals. References Doyle, L. (1995). What makes women sick? Macmillan, London. Coleman, et al. (1993). Ageing in the twentieth century, Sage: London Liu H and Shaffer D. (2004). The Effects of Gender and Age on Health. Macmillan, London. Steve Brindle (2007). Gender, Health and Age, retrieved on 7th January, from Wales Health statistics (2008). Health survey data 2008, retrieved on 7th January, from Appendixes log: C:\Documents and Settings\Administrator\Deskto > p\2222.smcl log type: smcl opened on: 7 Jan 2010, 04:27:08 . table health health Freq. 1 60 2 131 3 118 4 64 5 27 . table gender health health gender 1 2 3 4 5 0 28 65 60 35 12 1 32 66 58 29 15 . table age health health age 1 2 3 4 5 1 38 63 39 11 4 2 16 46 45 23 10 3 6 22 34 30 13 . graph pie, over(age) title(Age) . graph pie, over(age) title(Age) plabel(_all percent) . graph pie, over(health) title(Age) plabel(_all percent) . graph pie, over(health) title(Health) plabel(_all percent > ) . table health health Freq. 1 60 2 131 3 118 4 64 5 27 . table age age Freq. 1 155 2 140 3 105 . save "C:\Documents and Settings\Administrator\Desktop\dat > a used.dta", replace file C:\Documents and Settings\Administrator\Desktop\data u > sed.dta saved . twoway connected health age . scatter health age, sort . regress health age gender Source SS df MS Numb > er of obs = 400 F( > 2, 397) = 28.25 Model 62.148867 2 31.0744335 Prob > > F = 0.0000 Residual 436.628633 397 1.09982023 R-sq > uared = 0.1246 Adj > R-squared = 0.1202 Total 498.7775 399 1.25006892 Root > MSE = 1.0487 > ------------------- health Coef. Std. Err. t P>t [ > 95% Conf. Interval] > ------------------- age .4940887 .0658351 7.50 0.000 . > 3646596 .6235178 gender -.045 .1048723 -0.43 0.668 -. > 2511745 .1611745 _cons 1.763584 .1440026 12.25 0.000 1 > .480481 2.046687 > ------------------- . regress health age Source SS df MS Numb > er of obs = 400 F( > 1, 398) = 56.44 Model 61.946367 1 61.946367 Prob > > F = 0.0000 Residual 436.831133 398 1.09756566 R-sq > uared = 0.1242 Adj > R-squared = 0.1220 Total 498.7775 399 1.25006892 Root > MSE = 1.0476 > ------------------- health Coef. Std. Err. t P>t [ > 95% Conf. Interval] > ------------------- age .4940887 .0657676 7.51 0.000 . > 3647933 .623384 _cons 1.741084 .1339789 13.00 0.000 1 > .477689 2.004478 > ------------------- . regress health gender Source SS df MS Numb > er of obs = 400 F( > 1, 398) = 0.16 Model .2025 1 .2025 Prob > > F = 0.6879 Residual 498.575 398 1.25270101 R-sq > uared = 0.0004 Adj > R-squared = -0.0021 Total 498.7775 399 1.25006892 Root > MSE = 1.1192 > ------------------- health Coef. Std. Err. t P>t [ > 95% Conf. Interval] > ------------------- gender -.045 .1119241 -0.40 0.688 -. > 2650364 .1750364 _cons 2.69 .0791423 33.99 0.000 2 > .534411 2.845589 > ------------------- log: C:\Documents and Settings\HP LTop\My Documents\freelance work\academ > ia.smcl log type: smcl opened on: 13 Jan 2010, 08:01:50   . reg health gender   Source | SS df MS Number of obs = 400 F( 1, 398) = 0.34 Model | .4225 1 .4225 Prob > F = 0.5617 Residual | 498.355 398 1.25214824 R-squared = 0.0008 -------------+------------------------------ Adj R-squared = -0.0017 Total | 498.7775 399 1.25006892 Root MSE = 1.119   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .065 .1118994 0.58 0.562 -.1549878 .2849878 _cons | 2.57 .1769285 14.53 0.000 2.222169 2.917831 ------------------------------------------------------------------------------   . reg health age   Source | SS df MS Number of obs = 400 #NAME? Model | .276416256 1 .276416256 Prob > F = 0.6388 Residual | 498.501084 398 1.25251529 R-squared = 0.0006 -------------+------------------------------ Adj R-squared = -0.0020 Total | 498.7775 399 1.25006892 Root MSE = 1.1192   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0330049 .0702568 0.47 0.639 -.1051159 .1711258 _cons | 2.605616 .143124 18.21 0.000 2.324242 2.886989 ------------------------------------------------------------------------------   . ovtest (note: predicted health^2 dropped due to collinearity) (note: predicted health^3 dropped due to collinearity)   Ramsey RESET test using powers of the fitted values of health Ho: model has no omitted variables F(1, 397) = 4.33 Prob > F = 0.0381   . collin gender age   Collinearity Diagnostics   SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- gender 1.01 1.00 0.9933 0.0067 age 1.01 1.00 0.9933 0.0067 ---------------------------------------------------- Mean VIF 1.01   Cond Eigenval Index --------------------------------- 1 2.8352 1.0000 2 0.1203 4.8538 3 0.0445 7.9814 --------------------------------- Condition Number 7.9814 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.9933   . collin gender health   Collinearity Diagnostics   SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- gender 1.00 1.00 0.9992 0.0008 health 1.00 1.00 0.9992 0.0008 ---------------------------------------------------- Mean VIF 1.00   Cond Eigenval Index --------------------------------- 1 2.8335 1.0000 2 0.1242 4.7769 3 0.0423 8.1801 --------------------------------- Condition Number 8.1801 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.9992   . collin age health   Collinearity Diagnostics   SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- age 1.00 1.00 0.9994 0.0006 health 1.00 1.00 0.9994 0.0006 ---------------------------------------------------- Mean VIF 1.00   Cond Eigenval Index --------------------------------- 1 2.7973 1.0000 2 0.1474 4.3556 3 0.0552 7.1167 --------------------------------- Condition Number 7.1167 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.9994   . cor gender health (obs=400)   | gender health -------------+------------------ gender | 1.0000 health | 0.0291 1.0000     . corr age health (obs=400)   | age health -------------+------------------ age | 1.0000 health | 0.0235 1.0000     . reg health gender   Source | SS df MS Number of obs = 400 #NAME? Model | .4225 1 .4225 Prob > F = 0.5617 Residual | 498.355 398 1.25214824 R-squared = 0.0008 -------------+------------------------------ Adj R-squared = -0.0017 Total | 498.7775 399 1.25006892 Root MSE = 1.119   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .065 .1118994 0.58 0.562 -.1549878 .2849878 _cons | 2.57 .1769285 14.53 0.000 2.222169 2.917831 ------------------------------------------------------------------------------   . test gender   ( 1) gender = 0   F( 1, 398) = 0.34 Prob > F = 0.5617   . reg health age   Source | SS df MS Number of obs = 400 #NAME? Model | .276416256 1 .276416256 Prob > F = 0.6388 Residual | 498.501084 398 1.25251529 R-squared = 0.0006 -------------+------------------------------ Adj R-squared = -0.0020 Total | 498.7775 399 1.25006892 Root MSE = 1.1192   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0330049 .0702568 0.47 0.639 -.1051159 .1711258 _cons | 2.605616 .143124 18.21 0.000 2.324242 2.886989 ------------------------------------------------------------------------------   . test age   ( 1) age = 0   F( 1, 398) = 0.22 Prob > F = 0.6388   . reg health gender   Source | SS df MS Number of obs = 400 #NAME? Model | .4225 1 .4225 Prob > F = 0.5617 Residual | 498.355 398 1.25214824 R-squared = 0.0008 -------------+------------------------------ Adj R-squared = -0.0017 Total | 498.7775 399 1.25006892 Root MSE = 1.119   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .065 .1118994 0.58 0.562 -.1549878 .2849878 _cons | 2.57 .1769285 14.53 0.000 2.222169 2.917831 ------------------------------------------------------------------------------   . predict res, resid   . su res, details option details not allowed r(198);   . su res, detail   Residuals ------------------------------------------------------------- Percentiles Smallest 1% -1.7 -1.7 5% -1.7 -1.7 10% -1.635 -1.7 Obs 400 25% -.7 -1.7 Sum of Wgt. 400   50% .3 Mean -5.96e-10 Largest Std. Dev. 1.117591 75% .365 2.365 90% 1.365 2.365 Variance 1.24901 95% 2.3 2.365 Skewness .329727 99% 2.365 2.365 Kurtosis 2.417681   . reg health age   Source | SS df MS Number of obs = 400 #NAME? Model | .276416256 1 .276416256 Prob > F = 0.6388 Residual | 498.501084 398 1.25251529 R-squared = 0.0006 -------------+------------------------------ Adj R-squared = -0.0020 Total | 498.7775 399 1.25006892 Root MSE = 1.1192   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0330049 .0702568 0.47 0.639 -.1051159 .1711258 _cons | 2.605616 .143124 18.21 0.000 2.324242 2.886989 ------------------------------------------------------------------------------   . predict res1, resid   . sum res1, detail   Residuals ------------------------------------------------------------- Percentiles Smallest 1% -1.70463 -1.70463 5% -1.671626 -1.70463 10% -1.638621 -1.70463 Obs 400 25% -.6881281 -1.70463 Sum of Wgt. 400   50% .2953694 Mean -1.19e-09 Largest Std. Dev. 1.117755 75% .3613793 2.361379 90% 1.361379 2.361379 Variance 1.249376 95% 2.328374 2.361379 Skewness .3222608 99% 2.361379 2.361379 Kurtosis 2.397636   . means age   Variable | Type Obs Mean [95% Conf. Interval] -------------+---------------------------------------------------------- age | Arithmetic 400 1.875 1.796611 1.953389 | Geometric 400 1.70061 1.626841 1.777725 | Harmonic 400 1.538462 1.474653 1.608042 ------------------------------------------------------------------------   . means gender   Variable | Type Obs Mean [95% Conf. Interval] -------------+---------------------------------------------------------- gender | Arithmetic 400 1.5 1.45079 1.54921 | Geometric 400 1.414214 1.366789 1.463284 | Harmonic 400 1.333333 1.290981 1.378559 ------------------------------------------------------------------------   . disp (400/6)*((-.119^2) + (((1.016-3)^2)/4)) 64.6602   . disp (400/6)*((.4422^2)+(((2.83-3)^2)/4)) 13.51772   . histogram res, normal bin(50) (bin=50, start=-1.7, width=.0813)   . histogram res1, normal bin(50) (bin=50, start=-1.7046305, width=.0813202)   . boxcox gender Fitting comparison model   Iteration 0: log likelihood = -290.31654 Iteration 1: log likelihood = -282.34287 Iteration 2: log likelihood = -282.34081 Iteration 3: log likelihood = -282.34081   Fitting full model   Iteration 0: log likelihood = -290.31654 Iteration 1: log likelihood = -282.34287 Iteration 2: log likelihood = -282.34081 Iteration 3: log likelihood = -282.34081   Number of obs = 400 LR chi2(0) = 0.00 Log likelihood = -282.34081 Prob > chi2 = . ------------------------------------------------------------------------------ gender | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /theta | 3.59e-07 .2499524 0.00 1.000 -.4898974 .4898981 ------------------------------------------------------------------------------ Estimates of scale-variant parameters ---------------------------- | Coef. -------------+-------------- Notrans | _cons | .3465736 -------------+-------------- /sigma | .3465736 ----------------------------   --------------------------------------------------------- Test Restricted LR statistic P-Value H0: log likelihood chi2 Prob > chi2 --------------------------------------------------------- theta = -1 -290.31654 15.95 0.000 theta = 0 -282.34081 -0.00 1.000 theta = 1 -290.31654 15.95 0.000 ---------------------------------------------------------   . boxcox age Fitting comparison model   Iteration 0: log likelihood = -476.55241 Iteration 1: log likelihood = -460.34314 Iteration 2: log likelihood = -460.34228 Iteration 3: log likelihood = -460.34228   Fitting full model   Iteration 0: log likelihood = -476.55241 Iteration 1: log likelihood = -460.34314 Iteration 2: log likelihood = -460.34228 Iteration 3: log likelihood = -460.34228   Number of obs = 400 LR chi2(0) = 0.00 Log likelihood = -460.34228 Prob > chi2 = . ------------------------------------------------------------------------------ age | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /theta | .178937 .1453477 1.23 0.218 -.1059393 .4638133 ------------------------------------------------------------------------------ Estimates of scale-variant parameters ---------------------------- | Coef. -------------+-------------- Notrans | _cons | .5769721 -------------+-------------- /sigma | .4945748 ----------------------------   --------------------------------------------------------- Test Restricted LR statistic P-Value H0: log likelihood chi2 Prob > chi2 --------------------------------------------------------- theta = -1 -491.34333 62.00 0.000 theta = 0 -461.09513 1.51 0.220 theta = 1 -476.55241 32.42 0.000 ---------------------------------------------------------   . reg health gender age   Source | SS df MS Number of obs = 400 Model | .647450012 2 .323725006 Prob > F = 0.7727 Residual | 498.13005 397 1.25473564 R-squared = 0.0013 -------------+------------------------------ Adj R-squared = -0.0037 Total | 498.7775 399 1.25006892 Root MSE = 1.1201   ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gender | .0611164 .1123899 0.54 0.587 -.1598373 .2820701 age | .0298738 .0705544 0.42 0.672 -.1088331 .1685808 _cons | 2.519812 .2131152 11.82 0.000 2.100837 2.938787 ------------------------------------------------------------------------------   . rvfplot   . tsset time variable not set, use -tsset varname ...- r(111);   . tsset health gender repeated time values within panel r(451);   . predict res4, r   . edit   . gen lres = res4(_n-1) Unknown function res4() r(133);   . dwstat time variable not set, use -tsset varname ...- r(111);   . ac res4 time variable not set, use -tsset varname ...- r(111); Read More