Question

Last week, a political campaign aired a new TV ad promoting its candidate. The ad was aired a different number of times depending on the region. To decide how many times to air the ad next week, the campaign manager looked at the impact the ad had made in the different regions.
She tracked the number of times the ad had run in each region, x, and the increase of the candidate's approval rating in those regions, y.
The least squares regression line of this data set is:
y=0.578x–5.202
What approval rating does this line predict in a region where the ad is run 15 times?
Round your answer to the nearest thousandth.
points

Answer 1

To predict the candidate's approval rating in a region where the ad is run 15 times, we can use the least squares regression line equation provided:

\[
y = 0.578x - 5.202
\]

Here, \(x\) is the number of times the ad is run, and \(y\) is the predicted approval rating.

Substituting \(x = 15\) into the equation:

\[
y = 0.578(15) - 5.202
\]

Calculating \(0.578 \times 15\):

\[
0.578 \times 15 = 8.67
\]

Now, substituting this back into the equation:

\[
y = 8.67 - 5.202
\]

Calculating \(8.67 - 5.202\):

\[
y = 3.468
\]

Rounding to the nearest thousandth, the predicted approval rating is:

\[
\boxed{3.468}
\]