Q11. Which of the following is the estimated intercept for the regression?

A)   −9.45.

B)   −0.11.

C)   −2.86.

Q12. Which of the following statements is most accurate regarding the significance of the regression parameters at a 5% level of significance?

A)   The parameter estimates for the intercept are significantly different than zero. The slope coefficients for index and size are not significant.

B)   The parameter estimates for the intercept and the independent variable size are significantly different than zero. The coefficient for index is not significant.

C)   All of the parameter estimates are significantly different than zero at the 5% level of significance.

Q13. William Brent, CFA, is the chief financial officer for Mega Flowers, one of the largest producers of flowers and bedding plants in the Western United States. Mega Flowers grows its plants in three large nursery facilities located in California. Its products are sold in its company-owned retail nurseries as well as in large, home and garden “super centers”. For its retail stores, Mega Flowers has designed and implemented marketing plans each season that are aimed at its consumers in order to generate additional sales for certain high-margin products. To fully implement the marketing plan, additional contract salespeople are seasonally employed. 

For the past several years, these marketing plans seemed to be successful, providing a significant boost in sales to those specific products highlighted by the marketing efforts. However, for the past year, revenues have been flat, even though marketing expenditures increased slightly. Brent is concerned that the expensive seasonal marketing campaigns are simply no longer generating the desired returns, and should either be significantly modified or eliminated altogether. He proposes that the company hire additional, permanent salespeople to focus on selling Mega Flowers’ high-margin products all year long. The chief operating officer, David Johnson, disagrees with Brent. He believes that although last year’s results were disappointing, the marketing campaign has demonstrated impressive results for the past five years, and should be continued. His belief is that the prior years’ performance can be used as a gauge for future results, and that a simple increase in the sales force will not bring about the desired results. 

Brent gathers information regarding quarterly sales revenue and marketing expenditures for the past five years. Based upon historical data, Brent derives the following regression equation for Mega Flowers (stated in millions of dollars):

Expected Sales = 12.6 + 1.6 (Marketing Expenditures) + 1.2 (# of Salespeople)

Brent shows the equation to Johnson and tells him, “This equation shows that a $1 million increase in marketing expenditures will increase the independent variable by $1.6 million, all other factors being equal.” Johnson replies, “It also appears that sales will equal $12.6 million if all independent variables are equal to zero.”

In regard to their conversation about the regression equation:

A)   Brent’s statement is correct; Johnson’s statement is correct.

B)   Brent’s statement is correct; Johnson’s statement is incorrect.

C)   Brent’s statement is incorrect; Johnson’s statement is correct.

答案和详解如下：

Q11. Which of the following is the estimated intercept for the regression?

A)   −9.45.

B)   −0.11.

C)   −2.86.

Correct answer is C)

The t-statistic for testing the null hypothesis H₀:  β_i = 0 is t = (b_i − 0) / σ_i, where β_i is the population parameter for independent variable i, b_i is the estimated parameter, and σ_i is the parameter’s standard error.  Using the information provided, the estimated intercept can be computed as b₀ = t × σ₀ = −5.2 × 0.55 = −2.86.

Q12. Which of the following statements is most accurate regarding the significance of the regression parameters at a 5% level of significance?

A)   The parameter estimates for the intercept are significantly different than zero. The slope coefficients for index and size are not significant.

B)   The parameter estimates for the intercept and the independent variable size are significantly different than zero. The coefficient for index is not significant.

C)   All of the parameter estimates are significantly different than zero at the 5% level of significance.

Correct answer is C)

At 5% significance and 97 degrees of freedom (100 − 3), the critical t-value is slightly greater than, but very close to, 1.984.  The t-statistic for the intercept and index are provided as −5.2 and 2.1, respectively, and the t-statistic for size is computed as 0.6 / 0.18 = 3.33.  The absolute value of the all of the regression intercepts is greater than t_critical = 1.984.  Thus, it can be concluded that all of the parameter estimates are significantly different than zero at the 5% level of significance.

Q13. William Brent, CFA, is the chief financial officer for Mega Flowers, one of the largest producers of flowers and bedding plants in the Western United States. Mega Flowers grows its plants in three large nursery facilities located in California. Its products are sold in its company-owned retail nurseries as well as in large, home and garden “super centers”. For its retail stores, Mega Flowers has designed and implemented marketing plans each season that are aimed at its consumers in order to generate additional sales for certain high-margin products. To fully implement the marketing plan, additional contract salespeople are seasonally employed. 

For the past several years, these marketing plans seemed to be successful, providing a significant boost in sales to those specific products highlighted by the marketing efforts. However, for the past year, revenues have been flat, even though marketing expenditures increased slightly. Brent is concerned that the expensive seasonal marketing campaigns are simply no longer generating the desired returns, and should either be significantly modified or eliminated altogether. He proposes that the company hire additional, permanent salespeople to focus on selling Mega Flowers’ high-margin products all year long. The chief operating officer, David Johnson, disagrees with Brent. He believes that although last year’s results were disappointing, the marketing campaign has demonstrated impressive results for the past five years, and should be continued. His belief is that the prior years’ performance can be used as a gauge for future results, and that a simple increase in the sales force will not bring about the desired results. 

Brent gathers information regarding quarterly sales revenue and marketing expenditures for the past five years. Based upon historical data, Brent derives the following regression equation for Mega Flowers (stated in millions of dollars):

Expected Sales = 12.6 + 1.6 (Marketing Expenditures) + 1.2 (# of Salespeople)

Brent shows the equation to Johnson and tells him, “This equation shows that a $1 million increase in marketing expenditures will increase the independent variable by $1.6 million, all other factors being equal.” Johnson replies, “It also appears that sales will equal $12.6 million if all independent variables are equal to zero.”

In regard to their conversation about the regression equation:

A)   Brent’s statement is correct; Johnson’s statement is correct.

B)   Brent’s statement is correct; Johnson’s statement is incorrect.

C)   Brent’s statement is incorrect; Johnson’s statement is correct.

Correct answer is C)

Expected sales is the dependent variable in the equation, while expenditures for marketing and salespeople are the independent variables. Therefore, a $1 million increase in marketing expenditures will increase the dependent variable (expected sales) by $1.6 million. Brent’s statement is incorrect.

Johnson’s statement is correct. 12.6 is the intercept in the equation, which means that if all independent variables are equal to zero, expected sales will be $12.6 million.

thx