Scenario 2

A manager is trying to understand the relationship between the amount of money spent advertising a product (in thousands of dollars) and sales (in millions of dollars) using data for 8 months. The manager runs a regression model and obtains the following output. Notice that both sales and advertising are log-transformed.

Regression results for Log(Sales)

Summary measures

R-Square

0.9984

Adj R-Square

0.9981

Regression coefficients

Coefficient Std Err t-value p-value

Constant 1.4009 0.0103 135.8713 0.0000

Log(Advertising)0.2022 0.0033 61.2021 0.0000

1

This question referencesScenario 2.

At the 5% level of significance, is (log-) advertising useful for explaining sales?

Yes

No

Can't say.

2

This question referencesScenario 2.

Would your answer in the previous questionchangeif you conducted the test at the 1% level of significance?

Yes

No

Can't say.

3

This question referencesScenario 2.

Consider the number 0.2022 in the column titled "Coefficient".Provide a precise economic interpretation for this number.

As advertising expenditures increase by $1, sales increase by $0.2022.

As advertising expenditures increase by 1%, sales increase by 0.2022%.

As advertising expenditures increase by 1%, sales increase by 0.002022%.

As advertising expenditures increase by 1%, sales increase by $0.2022.

None of he above.

4

This question referencesScenario 2.

Construct a 95% confidence interval for the coefficient of Log(Advertising). The confidence interval equals...

(0.202; 1.401)

(0.171; 0.233)

(0.196; 0.209)

(0.192; 0.212)

None of the above.

5

This question referencesScenario 2.

If advertising expenditures are set at 20 thousand dollars, then estimated sales are

Approximately $231 million

Approximately 150 million

Approximately $7 million

Approximately $5 million

Approximately $4 million

6

This question referencesScenario 2.

What percentage of the total variation in sales isnotexplained by advertising?

More than 99%

50%

6%

2%

Less than 1%