Chapter 5

Which of the following statements is correct in relation to the above estimated model?

• If x3 increases by 1 unit, y declines by 0.72.

• If x2 falls by 2 per cent, log(y) increases by 68 per cent.

• If x1 increases by 1 unit, y rises by 25 per cent.

• When the values of x1, x2 and x3 are zero, the predicted value of y is 1.24.

The estimated regression line of y on x1 and x2 is: y = 7.9375 + 0.5625x1 - 0.6875x2 The sum of squared residuals (SSR) is given by:

• 0

• 6.19

• 1.42

• 23.14

Suppose that the following quadratic average cost function has been estimated for a clothing company making men’s business shirts based in Melbourne: ^ACi = − 40 15Y Y +1.9 , i i 2 where AC and Y stand for average cost (measured in dollars) and total output (measured in thousands of pieces), respectively. Which of the following statements is not true?

• If the total production is 1500 pieces, average cost per shirt is $21.78.

• As number of shirts produced is increased by 100 units, average cost per shirt increases by $26.90.

• The approximate change in average cost per shirt due to a unit change in production of shirt is −15 + 3.8Y.

• When the company produces 4000 shirts, its average cost is lower than when it produces 2000 shirts.

For a regression model with y as the dependent variable and x1, x2, x3 and x4 as the four explanatory variables, which of the following equations is incorrectly computed from the sum of squared residual function to be included in the OLS first order conditions?

• 
• 
• 
• 

• R2 = 0.74

• R2 = 0.26

• R2 = 0.77

• R2 = 0.22

Within the multiple regression modelling framework, the assumption of no perfect collinearity indicates that:

• the explanatory variables will not be correlated at all.

• the explanatory variables will have a correlation coefficient close to one.

• none of the independent variables will be an exact linear combination of the other independent variables.

• the explained variable will not be correlated with the other variables.

• 44

• 60

• 57

• 91

8 In the context of a multiple regression model with k independent variables, what happens to var(Bˆj ) for j = 1, 2, …, k when the linear relationship among the independent variables falls?

• var(Bˆj) increases.

• var(Bˆj) decreases.

• var(Bˆj) remains unchanged.

• var(Bˆj) cannot be computed.

• The means of the variables should lie on the fitted line for both the models.

• The sum squared residuals from model 2 would be higher than sum squared residuals from model 1.

• The OLS estimators in model 1 possess the minimum variance property.

• The R2 of model 2 would be lower than the R2 of model 1.

Adjusted R2 in the multiple regression model:

• always increases when an additional explanatory variable is added.

• will never be greater than the regression R2 .

• equals the square of the correlation coefficient r.

• cannot be negative.