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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]y[/tex] represents the company sales in dollars, about how much can the company expect in sales if it spends [tex]\$150[/tex] on advertising?

A. [tex]\$315[/tex]
B. [tex]\$130[/tex]
C. [tex]\$465[/tex]
D. [tex]\$445[/tex]

Sagot :

GinnyAnsweridn
To determine the expected sales [tex]\( y \)[/tex] when the company spends [tex]\( \$150 \)[/tex] on advertising, we will use the given linear regression equation:

[tex]\[ y = 2.1x + 130 \][/tex]

Here, [tex]\( x \)[/tex] is the amount of money spent on advertising, which is [tex]\( \$150 \)[/tex].

Let's substitute [tex]\( x = 150 \)[/tex] into the equation:

[tex]\[ y = 2.1 \cdot 150 + 130 \][/tex]

First, perform the multiplication:

[tex]\[ 2.1 \cdot 150 = 315 \][/tex]

Next, add the result to 130:

[tex]\[ y = 315 + 130 \][/tex]

[tex]\[ y = 445 \][/tex]

Therefore, the expected sales when the company spends [tex]\( \$150 \)[/tex] on advertising is [tex]\( \$445 \)[/tex].

Thus, the correct answer is:

D. \$445
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