Regression Analysis: Credit Balance Versus Income, Size, Years (Coursework Sample)

Regression and Correlation Analysis Regression Analysis: Credit balance versus Income, Size, Years Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 36973471 12324490 61.17 0.000 Income 1 9381778 9381778 46.57 0.000 Size 1 16682665 16682665 82.80 0.000 Years 1 216131 216131 1.07 0.305 Error 51 10275009 201471 Total 54 47248480 Model Summary S R-sq R-sq(adj) R-sq(pred) 448.855 78.25% 76.97% 74.60% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 1394 270 5.16 0.000 Income 29.53 4.33 6.82 0.000 1.14 Size 315.6 34.7 9.10 0.000 1.11 Years 13.0 12.6 1.04 0.305 1.07 Regression Equation Credit balance = 1394 + 29.53 Income + 315.6 Size + 13.0 Years Above are the regression analysis results 1 Perform the Global Test for Utility (F-Test). Explain your conclusion. The global test is usually used to test all β’s within a model. This is usually performed through F-test. In this f-test, the hypothesis to be tested will be; H0: β1=β2=β3= 0 Ha: at least one βj ≠ 0 Decision: reject H0 if p-value<0.05 From the regression analysis results, the F-statistic=61.17 with p-value=0.000. Therefore, we will reject the null hypothesis and conclude that at least one βj ≠ 0 at 0.05 level of significance 2 Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded. In order to perform this analysis, we will find the critical t-value and compare it with the computed t-statistic. Hypothesis test for β1; H0: β1= 0 Ha: β1≠ 0 Critical value, tα2,n-k=t0.025,52=2.009 Decision: reject H0 if tβ1>tα2,n-k Test statistic From the above table, tβ1=6.82 Since tβ1>tα2,n-k We will reject the null hypothesis and conclude that β1≠ 0 at 5% level of si...