Suppose the linear regression line [tex]$y = 2.1x + 130$[/tex] predicts sales based on the money spent on advertising. If [tex]$x$[/tex] represents the dollars spent on advertising, and [tex][tex]$y$[/tex][/tex] represents the company sales in dollars, about how much can the company expect in sales if it spends [tex]$\$250$[/tex] on advertising?

A. [tex]$\[tex]$250$[/tex][/tex]
B. [tex]$\$655$[/tex]
C. [tex]$\[tex]$525$[/tex][/tex]
D. [tex]$\$130$[/tex]



Answer :

To determine the expected sales based on the given linear regression equation, we follow these steps:

1. We are provided with the linear regression line equation [tex]\( y = 2.1x + 130 \)[/tex], where [tex]\( y \)[/tex] represents the company’s sales and [tex]\( x \)[/tex] represents the dollars spent on advertising.

2. To find the expected sales when the company spends \[tex]$250 on advertising, we substitute \( x = 250 \) into the equation. 3. Performing this substitution, we get: \[ y = 2.1 \times 250 + 130 \] 4. Next, we multiply \( 2.1 \) by \( 250 \): \[ 2.1 \times 250 = 525 \] 5. Adding the result to 130: \[ 525 + 130 = 655 \] Thus, the company can expect approximately \$[/tex]655 in sales if it spends \[tex]$250 in advertising. Therefore, the correct answer is: B. \$[/tex]655