Question

A large toy company introduces many new toys to its product line each year. The

company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the percent of customers who had heard of the product by the end of the second month after its introduction). A random sample of $65$new products was taken, and a correlation of $0.96$was computed. Which of the following is true?

a. The least-squares regression line accurately predicts first-year sales 96% of the time.

b. About $92\%$ of the time, the percent of people who have heard of the product by the end of the second month will correctly predict first-year sales.

c. About $92\%$ of first-year sales can be accounted for by the percent of people who have heard of the product by the end of the second month.

d. For each increase of 1% in awareness of the new product, the predicted sales will go up by $0.96$ million dollars.

e. About $92\%$ of the variation in first-year sales can be accounted for by the leastsquares regression line with the percent of people who have heard of the product by the end of the second month as the explanatory variable.

Short answer

The correct answer is

e. The leastsquares regression line with the $92\%$of persons who had heard of the product by the end of the second month as the explanatory variable may explain for around half of the variation in first-year sales.

Step-by-step solution

 Step 1: Given information 

We have to tell about percent of customers who had heard of the product by the end of the second month after its introduction.

Explanation 

Keep in mind that the value you've been provided is the correlation, not the slope. Some of the responses you've received are interpretations of the slope, and there's no way to compute the slope of the regression line with the data you've been given.

The coefficient of determination is R-sq, and because this is a simple linear regression (just one predictor), we can compute it by squaring the correlation coefficient.

In response e, the interpretation of the coefficient of determination (R-sq) is correct.