Statistics Project Module Analysis - Assignment Example

Statistics project 10.15 Learning Activity The overall goal of this learning activity is to visualize the relationship betweentwo scale variables creating scatterplots and to quantify this relationship with the correlation coefficient. In this set of learning activities you will use the data file Bank.sav. 1. Suppose you are interested in understanding how an employees demographic characteristics, beginning salary, and time at the bank and in the work force are related to current salary. Start by producing scatterplots of salbeg, sex, time, age, edlevel, and work with salnow. Add a fit line to each plot. Check on the variable labels for time and work so you understand what these variables are measuring. SOLUTION 2. Describe the relationships based on the scatterplots. Do they all appear to be linear? Are any relationships negative? What is the strongest relationship? SOLUTION Based on the graphs shown above, it is clear that only two graph (a scatter plot graph of current salary against beginning salary and that of current salary against education level) showed a strong positive linear relationship. The graphs of current salary against age and that of current salary against work experience showed a slight negative relationship. The other graphs do not show a clear linear relationship. The strongest relationship is between current salary and beginning salary. 3. Now produce correlations with all these variables. Which correlations with salnow are significant? What is the largest correlation in absolute value with salnow? Did this match what you thought based on the scatterplots? SOLUTION Correlations Beginning salary Sex of employee Job seniority Age of employee Current salary Educational level Work experience Beginning salary Pearson Correlation 1 -0.457 -0.020 -0.011 0.880 0.633 0.045 Sig. (2-tailed) 0.000 0.668 0.811 0.000 0.000 0.327 N 474 474 474 474 474 474 474 Sex of employee Pearson Correlation -0.457 1 -0.066 0.052 -0.450 -0.356 -0.165 Sig. (2-tailed) 0.000 0.148 0.259 0.000 0.000 0.000 N 474 474 474 474 474 474 474 Job seniority Pearson Correlation -0.020 -0.066 1 0.052 0.084 0.047 0.003 Sig. (2-tailed) 0.668 0.148 0.262 0.067 0.303 0.949 N 474 474 474 474 474 474 474 Age of employee Pearson Correlation -0.011 0.052 0.052 1 -0.146 -0.281 0.804 Sig. (2-tailed) 0.811 0.259 0.262 0.001 0.000 0.000 N 474 474 474 474 474 474 474 Current salary Pearson Correlation 0.880 -0.450 0.084 -0.146 1.000 0.661 -0.097 Sig. (2-tailed) 0.000 0.000 0.067 0.001 0.000 0.034 N 474 474 474 474 474 474 474 Educational level Pearson Correlation 0.633 -0.356 0.047 -0.281 0.661 1 -0.252 Sig. (2-tailed) 0.000 0.000 0.303 0.000 0.000 0.000 N 474 474 474 474 474 474 474 Work experience Pearson Correlation 0.045 -0.165 0.003 0.804 -0.097 -0.252 1 Sig. (2-tailed) 0.327 0.000 0.949 0.000 0.034 0.000 N 474 474 474 474 474 474 474 **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed). Variables with significant correlations with salnow at 5% level of significance are; beginning salary, sex of employee, age of employee, education level, and work experience. The largest correlation in absolute value with salnow is 0.880 (this was between salnow and salbeg). It matched what I thought based on the scatterplots. 11.16 Learning Activity The overall goal of this learning activity is to run linear regressions and to interpret the output. You will use the PASW Statistics data file Census.sav. 1. Run a linear regression to predict total family income (income06) with highest year of education (educ). First, do a scatterplot of these two variables and superimpose a fit line. Does the relationship seem linear? How would you characterize the relationship? SOLUTION From the above graph there seems to exist a linear relationship between total family income and the highest year of school completed. I would characterize the relationship as positive linear relationship. 2. Now run the linear regression. What is the Adjusted R square value? Is the regression significant? What is the B coefficient for educ? Interpret it. SOLUTION Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .363a .132 .131 5.652 a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 9386.634 1 9386.634 293.810 .000a Residual 61947.138 1939 31.948 Total 71333.772 1940 a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED b. Dependent Variable: TOTAL FAMILY INCOME 2006 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 7.948 .580 13.695 .000 HIGHEST YEAR OF SCHOOL COMPLETED .719 .042 .363 17.141 .000 a. Dependent Variable: TOTAL FAMILY INCOME 2006 The Adjusted R square value is 0.131. The regression is significant at 5% significance level since we observe the p-value to be 0.000 (a value less than α=0.05) leading to rejection of the null hypothesis and concluding that indeed the regression is significant at 5% significance level. The B coefficient for educ is 0.719; this implies that for any unit change in education level, the dependent variable (total family income) changes by 0.719. That is to say, if education level increases by one unit then we would expect the total family income to increase by 0.719 and vice versa. 3. Next add the variables born (born in the U.S. or overseas), age, sex, and number of brothers and sisters (sibs). Check the coding on born so you can interpret its coefficient. First, do a scatterplot of age and sibs with income06. Superimpose a fit line. Does the relationship seem linear? How would you characterize the relationship? Why not do scatterplots of income06 with sex and born? SOLUTION The relationship between total family income and number of brothers and sisters seems to be linear while that total family income and age does not seem to be linear. The relationship between total family income and number of brothers and sisters would be characterized as negative linear relationship. We do not construct scatterplots of income06 with sex and born as the variables (sex and born) are categorical and not scale. 4. Which variables are significant predictors? What is the effect of each on income06? Which variable is the strongest predictor? The weakest? SOLUTION Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .395a .156 .154 5.558 a. Predictors: (Constant), WAS R BORN IN THIS COUNTRY, RESPONDENTS SEX, AGE OF RESPONDENT, NUMBER OF BROTHERS AND SISTERS, HIGHEST YEAR OF SCHOOL COMPLETED ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 10970.131 5 2194.026 71.012 .000a Residual 59414.454 1923 30.897 Total 70384.585 1928 a. Predictors: (Constant), WAS R BORN IN THIS COUNTRY, RESPONDENTS SEX, AGE OF RESPONDENT, NUMBER OF BROTHERS AND SISTERS, HIGHEST YEAR OF SCHOOL COMPLETED b. Dependent Variable: TOTAL FAMILY INCOME 2006 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 7.510 1.009 7.441 .000 HIGHEST YEAR OF SCHOOL COMPLETED .702 .044 .356 15.927 .000 NUMBER OF BROTHERS AND SISTERS -.150 .043 -.079 -3.530 .000 RESPONDENTS SEX -.943 .254 -.078 -3.714 .000 AGE OF RESPONDENT .030 .008 .085 4.010 .000 WAS R BORN IN THIS COUNTRY 1.099 .388 .060 2.829 .005 a. Dependent Variable: TOTAL FAMILY INCOME 2006 From the regression analysis table (coefficients table) above, it is clear that all the predictor variables are significant at 5% significance level. The coefficient for highest year of school completed is 0.702 implying that for any unit change in education level, the dependent variable (total family income) changes by 0.702. That is to say, if education level increases by one unit then we would expect the total family income to increase by 0.702 and vice versa. The coefficient of born is 1.099 implying that for any unit change in born, the dependent variable (total family income) changes by 1.099. That is to say, if born level increases by one unit then we would expect the total family income to increase by 1.099 and vice versa. The coefficient for age is 0.03 implying that for any unit change in age, the dependent variable (total family income) changes by 0.03. That is to say, if age increases by one unit then we would expect the total family income to increase by 0.03 and vice versa. The coefficient for sibs is -0.15 implying that for any unit increase in the number of siblings, the dependent variable (total family income) decreases by 0.15. Lastly, the coefficient for sex is -0.943 implying that for any unit change in the sex units, the dependent variable (total family income) decreases by 0.943. The strongest predictor variable is highest year of school completed while the weakest predictor variable is the variable born (born in the U.S. or overseas). Read More