TB LAB Qu. 07-58 Based on Lab 7-9 Excel Evaluating...

Based on Lab 7-9 Excel Evaluating the Relationship between Sales and Advertising Expense and the regression results noted below where sales is the dependent variable and advertising is the independent variable, what is the expected payoff for every dollar of advertising expenses?

SUMMARY OUTPUT

Regression Statistics

Multiple R

           0.5359

R Square

           0.2872

Adjusted R Square

           0.2663

Standard Error

        6,938.73

Observations

36

ANOVA

df

SS

MS

F

Significance F

Regression

1

       659,621,859.21

       659,621,859.21

          13.7004

0.0008

Residual

34

   1,636,965,318.79

         48,146,038.79

Total

35

   2,296,587,178.00

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

   819,247.46

                 51,893.26

                          15.79

0.0000

713,788

924,707

713,788

924,707

Advertising Expenses

3.6776

0.9936

3.7014

0.0008

1.6584

5.6967

1.6584

5.6967

Question

TB LAB Qu. 07-58 Based on Lab 7-9 Excel Evaluating...

Based on Lab 7-9 Excel Evaluating the Relationship between Sales and Advertising Expense and the regression results noted below where sales is the dependent variable and advertising is the independent variable, what is the expected payoff for every dollar of advertising expenses?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.5359

R Square

0.2872

Adjusted R Square

0.2663

Standard Error

6,938.73

Observations

36

ANOVA

df

SS

MS

F

Significance F

Regression

1

659,621,859.21

13.7004

0.0008

Residual

34

1,636,965,318.79

48,146,038.79

Total

35

2,296,587,178.00

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

819,247.46

51,893.26

15.79

0.0000

713,788

924,707

713,788

924,707

Advertising Expenses

3.6776

0.9936

3.7014

0.0008

1.6584

5.6967

1.6584

5.6967

BlackTom AI · Accepted Answer

First, restating the essential question from the data provided: we have a regression where Sales is the dependent variable and Advertising Expenses is the independent variable. The regression coefficient for Advertising Expenses is 3.6776 with a standard error of 0.9936, and the intercept is 819,247.46. The goal is to interpret what the regression implies about the payoff for every dollar spent on advertising.

Option A: Every dollar invested in advertising expenses is associated with $0.99 in net income. This statement misinterprets the regression output. The coefficient 3.6776 describes the change in Sales (not net income) per additional dollar of Advertising Expenses, and there is no information here about net income or margins. Net income would require subtracting costs from sales, which is not provided by this simple Sales ~ Advertising model.

Option B: Every dollar invested in advertising expenses is associated with $3.67 in net income. Even though the intuition about 3.67 is close to the coefficient, the metric described—net income—is not what the regression estimates. The model predicts Sales, not net income, and it does not account for costs to determine profit or net income. So this phrasing uses the wrong dependent variable for the interpretation (net income instead of Sales).

Option C: Every dollar invested in advertising expenses is associated with $3.67 in sales. This aligns with the reported coefficient for Advertising Expenses, which is 3.6776. Rounding to two decimals gives 3.68, but conventionally you can say about $3.67. This reflects the estimated increase in Sales for each additional dollar of Advertising Expenses, given the units shown in the output.

Option D: Every dollar invested in advertising expenses is associated with $0.99 in sales. This value does not match the regression coefficient. There is no basis in the provided coefficients for a $0.99 sales effect per dollar; 0.99 would be far from the estimated slope and would imply a nearly flat or even inverse relationship, which the data do not support given the positive coefficient and the t-statistic.

Additional context that helps interpretation: the coefficient 3.6776 indicates a positive relationship; for every extra dollar spent on advertising, Sales are predicted to increase by about 3.6776 dollars. The standard error around that estimate (0.9936) suggests some uncertainty, but the t-statistic (approximately 3.7014) and the p-value (0.0008) imply the effect is statistically significant at conventional levels. The intercept tells us the expected Sales when Advertising Expenses are zero, but the question focuses on the incremental payoff per dollar, which is governed by the slope 3.6776.

In summary, the coefficient characterizes the marginal effect of Advertising on Sales, so the interpretation corresponds to the option describing about $3.67 in sales per extra dollar spent on advertising, not net income and not $0.99. The other options either misstate the unit (net income) or misstate the magnitude or direction of the relationship, conflicting with the regression output.

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