Question

Algebra 1

The director of marketing at a large company wants to determine if 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 $1,020 and Profit equal to $17,500? Round to the nearest integer.

Answer 1

Given:
Profit = 372.6 + 17.2(advertising dollars)
advertising dollars = 1,020
profit = 17,500

Profit = 372.6 + 17.2(advertising dollars)

We'll just input the amount specified in the equation.
17,500 = 372.6 + 17.2 (1020)
17,500 = 372.6 + 17,544
17,500 = 17,916.60

As you can see, the values do not equal. Its difference is the residual value.

17,916.60 - 17,500 = 416.60 residual value

Answer 2

$416.60

Explanation:

In this question the expression is given in the form of a regression line given: profit = 372.6 + 17.2×(advertising dollars)

We have to find the residual value for the advertising dollars spent

= $1,020 and profit = $17,500

We will calculate the profit for advertising dollars = $1,020

Profit = 372.6 + 17.2×(1020)

= 372.6 + 17544

= $17,916.6

But the profit is $17,500 so the difference in amount will be residual value

Residual value = 17,916.6 - 17,500 = $416.60

The value of residual is $416.60.