Question

multiple choice 4 points
select the most appropriate response.
a store manager conducted an experiment in which he systematically varied the width of a display for toothpaste from 3 ft. to 6 ft. and recorded the corresponding number
of tubes of toothpaste sold per day. the data was used to build a regression line, which was:
tubes sold per day = 20 + 10(display width)
what is the predicted number of tubes sold per day for a display width of 12 feet?
120
140
it would be unwise to use the regression line to make a prediction for a display width of 12 ft.

Explanation:

Step1: Analyze the regression line formula

The regression line formula is \( tubes\ sold\ per\ day=20 + 10(display\ width) \).

Step2: Substitute the display width value

We are asked to find the number of tubes sold per day for a display width of \( 12 \) feet. Substitute \( display\ width = 12 \) into the formula: \( tubes\ sold\ per\ day=20+10\times12 \).

Step3: Calculate the result

First, calculate \( 10\times12 = 120 \). Then, \( 20+120=140 \). But we need to check the range of the data used to build the regression line. The data for display width was from \( 3 \) ft to \( 6 \) ft. A display width of \( 12 \) ft is outside the range of the data used to create the regression line. Using the regression line to predict for a value outside the range of the explanatory variable (display width in this case) is not reliable.

Answer:

It would be unwise to use the regression line to make a prediction for a display width of \( 12 \) ft.