Question

the owner of a sporting goods store gathered data about the numbers of mens, womens and childrens bicycles sold each month. she used a graphing tool to organize the data in different scatter plots and found these lines of best fit: the relationship between the numbers of mens, x, and womens, y, bicycles sold is modeled by the equation y = 0.95x + 0.83, and the correlation coefficient for the data is 0.791. the relationship between the numbers of mens, x, and childrens, y, bicycles sold is modeled by the equation y = 0.87x + 0.98, and the correlation coefficient for the data is 0.564. the relationship between the numbers of childrens, x, and womens, y, bicycles sold is modeled by the equation y = 0.73x + 0.91, and the correlation coefficient for the data is 0.945. which line of best fit can the store owner expect to produce the most reliable predictions? a. the line modeling the numbers of mens and womens bicycles sold b. the line modeling the numbers of mens and childrens bicycles sold c. the line modeling the numbers of childrens and womens bicycles sold d. all three lines will give equally reliable predictions.

Explanation:

Step1: Recall correlation - coefficient concept

The closer the correlation coefficient is to 1 or - 1, the stronger the linear relationship and more reliable the line of best - fit for predictions.

Step2: Compare given correlation coefficients

We have correlation coefficients 0.791 for men's and women's bicycles, 0.564 for men's and children's bicycles, and 0.945 for children's and women's bicycles.

Step3: Determine the most reliable line

Since 0.945 is the closest to 1 among the three correlation coefficients, the line modeling the numbers of children's and women's bicycles sold is the most reliable for predictions.

Answer:

C. the line modeling the numbers of children's and women's bicycles sold