13.51 A doctor conducted a survey to define “healthy food items” based on the amount of sugar and fats contained in each item. From a sample of 25 items, the doctor collected the following output:

Parameter Coefficient Standard Deviation Constant 59.687 1.352 Carbohydrates - 2.124 1.053 Fats - 2.791 0.741 The doctor also estimated the following regression model:

yn = b0 + b1x1 + b2x2 where yn = Rating x1 = Amount of carbohydrates (in grams)

x2 = Amount of fats (in grams)

R2 = 0.713, F = 43.534 d = 3.15

a. The doctor is concerned about the possibility of multicollinearity. Explain whether it occurs in the model.

b. Use a hypothesis testing to show whether the model has uniform variance over the predicted values at 1% significance level.

c. Give one solution on how to deal with the conclusion you make in part

b. and why it will happen.

d. What method can be used to check whether the error terms in a model are autocorrelated?

e. Use the suggested method in part

c. to find out whether the error terms in the above model are negatively autocorrelated.