Question

A statistician wishes to estimate the price of a used car of a certain brand using linear regression based on the variables Age, Mileages, Crash history, and Owner’s plate number. To do so, she randomly selected a certain number of used cars of the brand and measures AGE, MILEAGE, CRASH HISTORY, and NUMBER OF DIGITS ON PLATE NUMBER. The following is the output from R. Based on the R output, answer the following questions.

Call: Im(formula = PRICE - AGE + MILEAGE + CRASH + PLATE_DIGITS) Residuals: Min 1Q Median 3Q Max -1.42685 -0.66292 0.00514 0.38230 1.67304 Coefficients: Estimate Std. Error t value Pr>lt) (Intercept) 20.57239 0.88363 23.282 5.83e-16 *** AGE 0.39639 0.33594 1.180 0.251865 MILEAGE -0.14315 0.03426 -4.178 0.000464 CRASH -1.59764 0.38917 -4.105 0.000550 PLATE_DIGITS -0.14590 0.25048 -0.582 0.566761 ** Signif. codes: ****' 0.001 "**' 0.01 "*' 0.05.' 0.1'1 Residual standard error: 0.9129 on 20 degrees of freedom Multiple R-squared: 0.9088, Adjusted R-squared: 0.8906 F-statistic: 49.82 on 4 and 20 DF, p-value: 4.017e-10

f) Which variable would you first eliminate to build a parsimonious model?

g) If we eliminate “PLATE DIGITS”, we get the R output on the next page. So, can we say this model is better than the preceding one? If so, what are the features that make the new model better than the preceding one?

h) Do you think it is reasonable to eliminate another predictor variable from the new model? If so, which predictor should be eliminated?

i) Common sense tells us “AGE”, “MILEAGE”, and “CRASH HISTORY” are important variables for PRICE prediction so why might we eliminate one of them from the model?

Answer 1

Result:

f) Which variable would you first eliminate to build a parsimonious model?

“PLATE DIGITS is the variable would first eliminate because it is not significant and has largest p value.

g) If we eliminate “PLATE DIGITS”, we get the R output on the next page. So, can we say this model is better than the preceding one? If so, what are the features that make the new model better than the preceding one?

R square adjusted for the first model is 0.8906 and the second model is 0.894. Second model have largest adjusted R square than the first model. Therefore the new model is better than the preceding one.

h) Do you think it is reasonable to eliminate another predictor variable from the new model? If so, which predictor should be eliminated?

Age is the non significant variable in the model( p value 0.30396 which is > 0.05 level). Therefore it is reasonable to eliminate AGE variable from the new model.

i) Common sense tells us “AGE”, “MILEAGE”, and “CRASH HISTORY” are important variables for PRICE prediction so why might we eliminate one of them from the model?

AGE is correlated with MILEAGE. Large AGE associated with large MILEAGE. Therefore we may eliminate one of them from the model.