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 in advertising, and [tex]y[/tex] represents the company sales in dollars, about how much can the company expect in sales if it spends [tex]\$50[/tex] in advertising?

A. [tex]\$650[/tex]
B. [tex]\$105[/tex]
C. [tex]\$323[/tex]
D. [tex]\$235[/tex]



Answer :

To determine how much the company can expect in sales if it spends [tex]$\$[/tex]50$ in advertising, we can use the given linear regression equation \( y = 2.1x + 130 \).

Here's the step-by-step process to solve the problem:

1. Identify the values given in the problem:
- \( x = 50 \) dollars (amount spent on advertising)

2. Substitute the value of \( x \) into the equation:
- The equation given is \( y = 2.1x + 130 \).

3. Perform the substitution:
[tex]\[ y = 2.1 \times 50 + 130 \][/tex]

4. Calculate the result of the multiplication:
- \( 2.1 \times 50 \) equals 105.

5. Add the constant term to the product:
[tex]\[ y = 105 + 130 \][/tex]

6. Perform the addition:
[tex]\[ y = 235 \][/tex]

Therefore, if the company spends \[tex]$50 on advertising, it can expect approximately \$[/tex]235 in sales.

The correct answer is:
D. [tex]$\$[/tex] 235$