An automobile financing company uses a rather complex credit rating system for car loans. The questionnaire requires substantial time to fill out, taking sales staff time and risking alienating the customer. The company decides to see whether three variables (age, monthly family income, and debt payments as a fraction of income) will reproduce the credit score reasonably accurately. Data were obtained on a sample (with no evident biases) of 500 applications. The complicated rating score was calculated and served as the dependent variable in a multiple ­regression. Some results from JMP are shown.
a. How much of the variation in ratings is accounted for by the three predictors?
b. Use this number to verify the computation of the overall F statistic.
c. Does the F test clearly show that the three independent variables have predictive value for the rating score?
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Reaponse Rating scare summary of Pit RSquare a] Root Hean Square Rror 2.023398 Hean or Response Cbservations cr Sum Wgts) 0979443 65:044 Farameter Estisazes Datimate std ErrOr t Ratio Probatt 54.657197 0.634731 86.10 0.0000 Intercept 0 011586 0.48 .6285 xonthly income Ο.0100597 0.000157 64.13 0.0000 239 0,883684 45.21 .0000 Debt traction 9.95 Eitect Test Npam DF Sum or Squares Ratto PP 0.960 0.2344 0.6285 16835.19S 4112.023 0.0000 8363.627 2044.05 0.0000 ource Nentnly incone Debt frastion 1 hale-Modal Test 100 40 30 40 50 0 70 90 90 100 Rating score Predicted analyeis of variance DF Sum of squars 97349 239 2030.63 99379,032 Squara Ratia 22449.4 7925.929 Model 496 4 Prob C Total 49 0.0000