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:
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Brent’s statement is correct; Johnson’s statement is correct. | |
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Brent’s statement is incorrect; Johnson’s statement is correct. | |
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Brent’s statement is correct; Johnson’s statement is incorrect. | |
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. (Study Session 3, LOS 12.a)
Using data from the past 20 quarters, Brent calculates the t-statistic for marketing expenditures to be 3.68 and the t-statistic for salespeople at 2.19. At a 5% significance level, the two-tailed critical values are tc = +/- 2.127. This most likely indicates that:
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the t-statistic has 18 degrees of freedom. | |
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both independent variables are statistically significant. | |
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the null hypothesis should not be rejected. | |
Using a 5% significance level with degrees of freedom (df) of 17 (20-2-1), both independent variables are significant and contribute to the level of expected sales. (Study Session 3, LOS 12.a)
Brent calculated that the sum of squared errors (SSE) for the variables is 267. The mean squared error (MSE) would be:
The MSE is calculated as SSE / (n – k – 1). Recall that there are twenty observations and two independent variables. Therefore, the MSE in this instance [267 / (20 – 2 - 1)] = 15.706. (Study Session 3, LOS 11.i)
Brent is trying to explain the concept of the standard error of estimate (SEE) to Johnson. In his explanation, Brent makes three points about the SEE:
- Point 1: The SEE is the standard deviation of the differences between the estimated values for the independent variables and the actual observations for the independent variable.
- Point 2: Any violation of the basic assumptions of a multiple regression model is going to affect the SEE.
- Point 3: If there is a strong relationship between the variables and the SSE is small, the individual estimation errors will also be small.
How many of Brent’s points are most accurate?
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1 of Brent’s points are correct. | |
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All 3 of Brent’s points are correct. | |
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2 of Brent’s points are correct. | |
The statements that if there is a strong relationship between the variables and the SSE is small, the individual estimation errors will also be small, and also that any violation of the basic assumptions of a multiple regression model is going to affect the SEE are both correct.
The SEE is the standard deviation of the differences between the estimated values for the dependent variables (not independent) and the actual observations for the dependent variable. Brent’s Point 1 is incorrect.
Therefore, 2 of Brent’s points are correct. (Study Session 3, LOS 11.f)
Assuming that next year’s marketing expenditures are $3,500,000 and there are five salespeople, predicted sales for Mega Flowers will be:
Using the regression equation from above, expected sales equals 12.6 + (1.6 x 3.5) + (1.2 x 5) = $24.2 million. Remember to check the details – i.e. this equation is denominated in millions of dollars. (Study Session 3, LOS 12.c)
Brent would like to further investigate whether at least one of the independent variables can explain a significant portion of the variation of the dependent variable. Which of the following methods would be best for Brent to use?
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The multiple coefficient of determination. | |
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To determine whether at least one of the coefficients is statistically significant, the calculated F-statistic is compared with the critical F-value at the appropriate level of significance. (Study Session 3, LOS 12.e) | 
发表于 2010-4-8 13:58
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