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:
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.
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.
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?
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.
To find the value of the residual, we need to substitute the given values of advertising dollars and profit into the regression line equation and calculate the difference between the predicted profit and the actual profit.
Given:
Advertising dollars (x) = $1020
Profit (y) = $17500
The regression line equation is:
Profit = 372.6 + 17.2(Advertising dollars)
Substitute the values into the equation:
Profit = 372.6 + 17.2($1020)
Profit ≈ 372.6 + 17.2(1020)
Profit ≈ 372.6 + 17.2(1020)
Profit ≈ 372.6 + 17544
Profit ≈ 17916.6
Now, we can calculate the residual by subtracting the predicted profit from the actual profit:
Residual = Actual profit - Predicted profit
Residual = $17500 - $17916.6
Residual ≈ -$416.6
Rounding to the nearest integer, the value of the residual for advertising dollars spent equal to $1020 and profit equal to $17500 is approximately -$417.