Read the following description of a data set.

An automobile dealership ran a radio ad campaign to help sell its least popular model. The dealership always used the same ad but broadcast it a different number of times each week.
The sales manager tallied the number of ads broadcast each week, x, and the weekly sales of the model, y.
The least squares regression line of this data set is:
y=0.593x+4.936
How many sales of the model does this line predict for a week where the ad is broadcast 14 times?
Round your answer to the nearest integer.
cars

1 answer

To predict the number of sales when the ad is broadcast 14 times, we will use the given least squares regression line equation:

\[ y = 0.593x + 4.936 \]

Substituting \(x = 14\) into the equation:

\[ y = 0.593(14) + 4.936 \]

Now calculating \(0.593 \times 14\):

\[ 0.593 \times 14 = 8.302 \]

Now, add this result to 4.936:

\[ y = 8.302 + 4.936 = 13.238 \]

Rounding 13.238 to the nearest integer gives:

\[ y \approx 13 \]

Thus, the predicted number of sales for a week where the ad is broadcast 14 times is 13 cars.