Chapter 10, Problem AP3.19CPT

To determine

The true statement is to be choose which shows the interpretation of correlation and random sample of new products of Toy Company.

1. Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.
2. About $\text{92}\%$ 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.
3. About $\text{92}\%$ 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’s month.
4. For each increase of $1\%$ in awareness of the new product, the predicted sales will go up by $0.96$ million dollars.
5. About of $\text{92}\%$ the variation in first-year sales can be accounted for by the least-squares regression line with percent of people who have heard of the product by the end of the second month as the explanatory variable.

Answer to Problem AP3.19CPT

The true statement is (e).About $\text{92}\%$ of the variation in first-year sales can be accounted for by the least-squares regression line with percent of people who have heard of the product by the end of the second month as the explanatory variable.

Explanation of Solution

Given:

Correlation value: $r=0.96$

Take close look that the value given to you is correlation and not the slope. Some of the answers given you are explanations of the slope and there is no way to compute the slope of the regression line based on the available data.

  $R^2=r^2={0.96}^2=0.92$

The factor of determination is $R^2$ , since this is a simple linear regression only one analyst which can compute the coefficient of determination by squaring the correlation coefficient.

The coefficient of determination is the proportion of total variance that's explained by the model. Only answer (e) displays this that’s why the true statement is (e).

Conclusion:

Hence, true statement is shown by option (e).