the director of marketing at a large company wants to determine the amount of money spent on internet marketing is a good predictor of company profit. She fits a least-squares regression line to 20 months of data and computes the following regression line:

Question

Profit=372.6+17.2(advertising dollars)
What is the value of the residual for advertising dollars spent equal to $1020 and profit equal to 17500? Round to the nearest integer.

Answer 1

To find the residual, we need to use the regression line equation and substitute the given values for advertising dollars and profit:

Profit = 372.6 + 17.2(1020)
Profit = 372.6 + 17544
Profit = 17916.6

The predicted profit for advertising dollars spent equal to $1020 is $17916.6. To find the residual, we subtract the predicted value from the actual value:

Residual = Actual profit - Predicted profit
Residual = 17500 - 17916.6
Residual = -416.6

Therefore, the value of the residual for advertising dollars spent equal to $1020 and profit equal to 17500 is approximately -417.

Answer 2

a professor determined the relationship between the time spent studying (in hours) and performance on an exam.
performance=70.443+4.885*(time)
Ann studied 2.6 hours for the last exam. However, there was a concert in town the night before and her score was 16 points lower than expected. what was her score on this exam, rounded to the nearest integer?

Answer 3

We can use the regression line equation to find the expected score if Ann studied 2.6 hours:

Expected score = 70.443 + 4.885*(2.6)
Expected score = 83.3518

However, Ann's actual score was 16 points lower than expected, so we need to subtract 16 from the expected score:

Actual score = Expected score - 16
Actual score = 83.3518 - 16
Actual score = 67.3518

Rounding to the nearest integer, Ann's score on this exam was 67.