Question

A consumer protection group compares three types of front bumpers for a brand of automobile. It compares three bumpers, with sample mean damages of 2 for Bumper A, 3 for Bumper B, and 13 for Bumper C (in hundreds of dollars). Report the prediction equation you would obtain for the regression model. Use Bumper A as the reference group.

A. yhat = 1 + 2 X1 + 3 X2 + 13 X3, where X1 is an indicator for Bumper A, X2 is an indicator for Bumper B, and X3 is an indicator for Bumper C.

B. yhat = 1 + 2 X1+ 3 X2, where X1 is an indicator for Bumper A and X2 is an indicator for Bumper B.

C. yhat = 2 + 1 X1 + 11 X2, where X1 is an indicator for Bumper B and X2 is an indicator for Bumper C.

D. yhat = 2 + 3 X1 + 13 X2, where X1 is an indicator for Bumper B and X2 is an indicator for Bumper C.

Answer 1

Given:

Bumper A = X1 = sample mean=2

Bumper B= X2= Sample mean=3

Bumpee C= X3 = Sample mean = 13

Note: use Bumper A as the reference group, so value for assign bumper A =2 will be our intercept and X1 will be bumper 2, X2 will be bumper 3

Hence we get,

Yhat = 2 +  3X1 + 13X2

Option D) is correct