High School

An estate agent made a scatter plot with homeowners' property taxes on the [tex]y[/tex]-axis and the sizes of their homes, in square feet, on the [tex]x[/tex]-axis. The variables have a strong linear correlation, and the equation for the least squares regression line is [tex]2.098x - 254.098[/tex].

Based on the equation, what should the agent expect the property taxes to be for a 1300-square-foot home in the area?

A. \[tex]\$1045.90\]

B. \[tex]\$1554.10\]

C. \[tex]\$2473.30\]

Answer :

To find the expected property taxes for a 1300-square-foot home, we use the equation of the least squares regression line provided:

[tex]\[ y = 2.098x - 254.098 \][/tex]

In this equation:
- [tex]\( y \)[/tex] represents the property taxes,
- [tex]\( x \)[/tex] represents the size of the home in square feet.

Since we are looking for the property taxes of a 1300-square-foot home, we substitute [tex]\( x = 1300 \)[/tex] into the equation:

1. Multiply the size of the home by the slope of the line:
[tex]\[
2.098 \times 1300 = 2727.4
\][/tex]

2. Subtract the y-intercept from this product:
[tex]\[
2727.4 - 254.098 = 2473.302
\][/tex]

Therefore, the expected property taxes for a 1300-square-foot home in the area are approximately \$2473.30.

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