Price of a refrigerator (PRICE) in dollars can be explained by its characteristics such as annual cost of operation (OPCOST) in dollars, total size in cubic feet of the refrigerator (REFRSIZE) [the total size = the size of the freezer + the size of the non-frozen cooling compartment], size in cubic feet of the freezer (FREZSIZE), number of shelves (SHELVES), and number of features like egg racks and ice makers (FEATURES).

We have data on these variables for a set of refrigerators in the file problem3.xlsx.

Use Excel to estimate the model:

PRICE = b0 + b1OPCOST + b2REFRSIZE + b3FREZSIZE + b4SHELVES + b5FEATURES

(a) Report and interpret the coefficient of FREZSIZE.

(b) Predict the price of an average refrigerator. That is, predict the price of a refrigerator that has "average values" for the various characteristics. And, build a 95% confidence interval for the prediction.

(c) What is the probability that the predicted price in part (b) falls between $550 and $650?

Please show your calculation.

(d) It is of interest to study how price of refrigerator changes with a change in proportion of freezer size vis--vis the total refrigerator size.

Modify the regression equation to answer the following question...

Keeping the total refrigerator size constant, what is the percentage impact on PRICE for every percentage increase in the proportion of freezer size vis--vis the total refrigerator size.

Clearly write down your regression equation, and answer the question asked.