土豆妮

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) SALES = α + β1 POP + β2 INCOME + β3 ADV + ε.

C) INCOME = α + β1 POP + β2 SALES + β3 ADV + ε.

土豆妮

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) SALES = α + β1 POP + β2 INCOME + β3 ADV + ε.

C) INCOME = α + β1 POP + β2 SALES + β3 ADV + ε.

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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.

土豆妮

 

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% confidence level is 2.120.  Which of the independent variables is statistically different from zero at the 95% confidence level?

A) ADV only.

B) INCOME only.

C) INCOME and ADV.

土豆妮

 

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% confidence level is 2.120.  Which of the independent variables is statistically different from zero at the 95% confidence level?

A) ADV only.

B) INCOME only.

C) INCOME and ADV.

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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.

土豆妮

Consider the following regression equation:

Sales_i = 20.5 + 1.5 R&D_i + 2.5 ADV_i – 3.0 COMP_i

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) One more competitor will mean $3 million less in sales (holding everything else constant).

B) If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million.

C) If R&D and advertising expenditures are $1 million each and there are 5 competitors, expected sales are $9.5 million.

土豆妮

Consider the following regression equation:

Sales_i = 20.5 + 1.5 R&D_i + 2.5 ADV_i – 3.0 COMP_i

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) One more competitor will mean $3 million less in sales (holding everything else constant).

B) If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million.

C) If R&D and advertising expenditures are $1 million each and there are 5 competitors, expected sales are $9.5 million.

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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.

土豆妮

Consider the following regression equation:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i
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, COMP is the number of competitors in the industry, and CAP is the capital expenditures for the period in millions of dollars. 

Which of the following is NOT a correct interpretation of this regression information?

A) If a company spends $1 million more on capital expenditures (holding everything else constant), Sales are expected to increase by $8.0 million.

B) If R&D and advertising expenditures are $1 million each, there are 5 competitors, and capital expenditures are $2 million, expected Sales are $8.25 million.

C) One more competitor will mean $2 million less in Sales (holding everything else constant).

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Predicted sales = $10 + 1.25 + 1 – 10 + 16 = $18.25 million.

土豆妮

Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i

where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero?

A) R&D, ADV, COMP, and CAP.

B) ADV and CAP only.

C) R&D, COMP, and CAP only.

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The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% 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.

土豆妮

Consider the following regression equation:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i
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, COMP is the number of competitors in the industry, and CAP is the capital expenditures for the period in millions of dollars. 

Which of the following is NOT a correct interpretation of this regression information?

A) If a company spends $1 million more on capital expenditures (holding everything else constant), Sales are expected to increase by $8.0 million.

B) If R&D and advertising expenditures are $1 million each, there are 5 competitors, and capital expenditures are $2 million, expected Sales are $8.25 million.

C) One more competitor will mean $2 million less in Sales (holding everything else constant).

土豆妮

Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i

where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero?

A) R&D, ADV, COMP, and CAP.

B) ADV and CAP only.

C) R&D, COMP, and CAP only.