16.Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): SALES = 0.000 + 0.004 POP + 1.031 INCOME + 2.002 ADV | (0.113) | (0.005) | (0.337) | (2.312) | |
For next year, Hilton estimates the following parameters: (1) the population under 20 will be 120 million, (2) disposable income will be $300,000,000, and (3) advertising expenditures will be $100,000,000. Based on these estimates and the regression equation, what are predicted sales for the industry for next year? A) $557,143,000. B) $509,980,000. C) $656,991,000. D) $669,471,000. The correct answer was B) Predicted sales for next year are: SALES = α + 0.004 (120) + 1.031 (300) + 2.002 (100) = 509,980,000. 17.Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): SALES = α + 0.004 POP + 1.031 INCOME + 2.002 ADV | (0.005) | (0.337) | (2.312) | |
The critical t-statistic for a 95 percent confidence level is 2.120. Which of the independent variables is statistically different from zero at the 95 percent confidence level? A) INCOME and ADV. B) POP and ADV. C) INCOME only. D) ADV only. The correct answer was C) The calculated test statistic is coefficient/standard error. Hence, the t-stats are 0.8 for POP, 3.059 for INCOME, and 0.866 for ADV. Since the t-stat for INCOME is the only one greater than the critical t-value of 2.120, only INCOME is significantly different from zero. 18.Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years. Which of the follow regression equations correctly represents Hilton’s hypothesis? A) SALES = α x β1 POP x β2 INCOME x β3 ADV x ε. B) INCOME = α + β1 POP + β2 SALES + β3 ADV + ε. C) INCOME = α + β1 POP + β2 ADV + ε. D) SALES = α + β1 POP + β2 INCOME + β3 ADV + ε. The correct answer was D) SALES is the dependent variable. POP, INCOME, and ADV should be the independent variables (on the right hand side) of the equation (in any order). Regression equations are additive. 19.Consider the following regression equation: Salesi = 20.5 + 1.5 R&Di + 2.5 ADVi – 3.0 COMPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, and COMP is the number of competitors in the industry. Which of the following is NOT a correct interpretation of this regression information? A) If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. B) If R&D and advertising expenditures are $1 million each and there are 5 competitors, expected sales are $9.5 million. C) One more competitor will mean $3 million less in sales (holding everything else constant). D) Increasing advertising dollars by $1 million (holding everything else constant), will result in $2.5 million additional sales. The correct answer was A) If a company spends $1 million more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. Always be aware of the units of measure for the different variables. 20.Consider the following estimated regression equation, with standard errors of the coefficients as noted: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where the standard error for R&D is 0.45, the standard error for ADV is 2.2 , the standard error for COMP is 0.63, and the standard error for CAP is 2.5. The equation was estimated over 40 companies. Using a 5 percent level of significance, which of the independent variables significantly different from zero? A) R&D, ADV, COMP, and CAP. B) COMP and CAP only. C) R&D, COMP, and CAP only. D) ADV and CAP only. The correct answer was C) The critical t-values for 40-4-1 = 35 degrees of freedom and a 5 percent level of significance are ± 2.03. The calculated t-values are:
t for R&D = 1.25 / 0.45 = 2.777
t for ADV = 1.0/ 2.2 = 0.455
t for COMP = -2.0 / 0.63 = -3.175
t for CAP = 8.0 / 2.5 = 3.2
Therefore, R&D, COMP, and CAP are statistically significant. | 
发表于 2008-4-8 16:36
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