Multiple Regression Analysis - the Relationship between Per Capita and the Variables - Statistics Project Example

Statistics Multiple regressions dlypci 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui To beginwith, we need to find the relationship between the dependent variables and independent variable. From the correlation output table below we can note that there is a negative relationship between per capita GDP and inflation as well as proportion of secondary school age population enrolled at secondary school in 1990. This means that this two factors help to reduce the crime rate of the property. However per capital income of each state, high school drop out rate unemployment level, public aid for families with children and percentage of residents living in urban area have a positive relationship with property crime. It should be noted that percentage of residents living in an urban area and school drop out has stronger positive relationship with property crime than other factors. H0:2=3=4=5=6=7=0 against H1:j0 for at least one j(2...7), using a significance level of 0.05. The multiple regression analysis table below shows the relationship between per capita and the variables. SUMMARY OUTPUT Regression Statistics Multiple R 0.830892 R Square 0.690381 Adjusted R Square 0.629967 Standard Error 749.3944 Observations 50 ANOVA   df SS MS F Significance F Regression 8 51341130 6417641 11.42759 2.42E-08 Residual 41 23025269 561591.9 Total 49 74366399         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -642.503 1024.034 -0.62742 0.533861 -2710.58 1425.576 -2710.58 1425.576 lypc90 -0.01835 0.077307 -0.23731 0.813599 -0.17447 0.137779 -0.17447 0.137779 lseced 81.29257 21.98576 3.697511 0.000639 36.89144 125.6937 36.89144 125.6937 govgdp -113.714 78.70003 -1.44491 0.156083 -272.652 45.2235 -272.652 45.2235 openi -1.98415 0.729924 -2.71829 0.009573 -3.45826 -0.51003 -3.45826 -0.51003 infli 1.103845 1.448536 0.762042 0.450397 -1.82153 4.029223 -1.82153 4.029223 crediti 1.582106 11.16358 0.14172 0.887995 -20.9632 24.12741 -20.9632 24.12741 dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui where ypc05 = per capita GDP (constant prices, chain series) in 2005 ypc90 = per capita GDP (constant prices: chain series) in 1990 dlypc = ln(ypc05) – ln(ypc90) lypc90 = ln(ypc90) seced = proportion of secondary school age population enrolled at secondary school in 1990 lseced = ln(seced) govgdp = government share of real GDP per capita in 1990 open = openness = ratio of (exports+imports) to GDP in 1990 cpi90 = consumer price index value in 1990 cpi85 = consumer price index value in 1985 infl = five-year inflation rate = ln(cpi90) – ln(cpi85) credit = ratio of private credit by deposit money banks and other financial institutions to GDP in 1990 The regression equation which can be formed using the above coefficients is dlypci = 81.29lsecedi -642.50 -0.018lypc90i -113.71govgdpi -1.98openi + 1.104infli + 1.58crediti + 749 An implication that some factors contributes to per capita GDP while other reduce. The coefficient of determination of the regression is 0.6903 meaning that there is a positive expectation that 69.03% of the variables have been included in the regression. Its common understanding that per capita GDP tend to reduce with inflation. If we compare the values in the tables it is noted that there is a difference which can be explained by the ability of the regression to predict the variations assessed by value of coefficient of determination. H0:2=0 against H0:20 using a significance level of 0.05. Given that the mean ln(proportion of secondary school age population enrolled at secondary school in 1990) is 81.29 and the rejection rules, and the table appended in Appendix, we can conclude that the population means are is not equal to zero. This conclusion is based on the fact that z = -0.43897 which is outside of the rejection region. Alternatively, the p-value for the test, labeled P(Z> Normally distributed >>> Homoscedastic References Aron, A., Aron, E., & Coups, E. J. (2006). Statistics for psychology. Pearson: Pearson Prentice Hall. Bluman, A. (2006). ELEMENTARY STATISTICS: A STEP BY STEP APPROACH. Boston: McGraw Hill Higher education Gore, S., & Altman, D.G., (1992). Statistics in Practice. London: British Medical Association. New York: Wiley, Read More