aianjie

 

The correct answer is A

Y = 2.83 + (1.5)(2)

= 2.83 + 3

= 5.83

aianjie

 

7、Paul Frank is an analyst for the retail industry. He is examining the role of television viewing by teenagers on the sales of accessory stores. He gathered data and estimated the following regression of sales (in millions of dollars) on the number of hours watched by teenagers (TV, in hours per week):

Salest = 1.05 + 1.6 TVt

The predicted sales if television watching is 5 hours per week is:

A) $8.00 million.

B) $9.05 million.

C) $2.65 million.

D) $1.05 million.

aianjie

 

The correct answer is B

The predicted sales are: Sales = $1.05 + [$1.6 (5)] = $1.05 + $8.00 = $9.05 million.

aianjie

 

The correct answer is B

The interpretation of the slope coefficient is the change in the dependent variable (sales in millions of dollars) for a given one-unit change in the independent variable (TV hours per week). The intercept of 1.05 means that 1.05 million dollars worth of accessories is expected to be sold even if TV watching is zero.

aianjie

 

4、An analyst is examining the relationship between two random variables, RCRANTZ and GSTERN. He performs a linear regression that produces an estimate of the relationship:

RCRANTZ = 61.4 ? 5.9GSTERN

Which interpretation of this regression equation is least accurate?

A) The covariance of RCRANTZ and GSTERN is negative.

B) If GSTERN increases by one unit, RCRANTZ should increase by 5.9 units.

C) The intercept term implies that if GSTERN is zero, RCRANTZ is 61.4.

D) In this regression, RCRANTZ is the dependent variable and GSTERN is the independent variable.

aianjie

 

The correct answer is B

The slope coefficient in this regression is -5.9. This means a one unit increase of GSTERN suggests a decrease of 5.9 units of RCRANTZ. The slope coefficient is the covariance divided by the variance of the independent variable. Since variance (a squared term) must be positive, a negative slope term implies that the covariance is negative.

aianjie

 

5、A simple linear regression is run to quantify the relationship between the return on the common stocks of medium sized companies (Mid Caps) and the return on the S& 500 Index, using the monthly return on Mid Cap stocks as the dependent variable and the monthly return on the S& 500 as the independent variable. The results of the regression are shown below:

	Coefficient	Standard Error of Coefficient	t-Value
Intercept	1.71	2.950	0.58
S& 500	1.52	0.130	11.69
R2 = 0.599

Use the regression statistics presented above and assume this historical relationship still holds in the future period. If the expected return on the S& 500 over the next period were 11%, the expected return on Mid Cap stocks over the next period would be:

A)    18.4%.

B)    33.8%.

C)   25.6%

D)   20.3%.

aianjie

 

AIM 3: Define and interpret the population regression function, regression coefficients, parameters, slope and the intercept.

1、Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R2 value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm’s sales during the following period does the regression model predict?

A) +0.72%.

B) +1.00%.

C) +0.65%.

D) +0.10%.

aianjie

 

The correct answer is B

The slope of the regression represents the linear relationship between the independent variable (the percent change in sales people) and the dependent variable, while the intercept represents the predicted value of the dependent variable if the independent variable is equal to zero. In this case, the percentage change in sales is equal to: 0.72(0) + 0.01 = +0.01.

aianjie

 

2、In the estimated regression equation Y = 0.78 - 1.5 X, which of the following is least accurate when interpreting the slope coefficient?

A) If the value of X is zero, the value of Y will be -1.5.

B) The dependent variable declines by -1.5 units if X increases by 1 unit.

C) The dependent variable increases by 1.5 units if X decreases by 1 unit.

D) -1.5 is the elasticity of Y with respect to X.