select the correct answer.\nthe owner of a sporting - goods store gathered data about the numbers of mens…

select the correct answer.\nthe 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:\n- 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 $0.791$.\n- 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 $0.564$.\n- 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 $0.945$.\nwhich line of best fit can the store owner expect to produce the most reliable predictions?\na. the line modeling the numbers of mens and womens bicycles sold\nb. the line modeling the numbers of mens and childrens bicycles sold\nc. the line modeling the numbers of childrens and womens bicycles sold\nd. all three lines will give equally reliable predictions.

select the correct answer.\nthe 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:\n- 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 $0.791$.\n- 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 $0.564$.\n- 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 $0.945$.\nwhich line of best fit can the store owner expect to produce the most reliable predictions?\na. the line modeling the numbers of mens and womens bicycles sold\nb. the line modeling the numbers of mens and childrens bicycles sold\nc. the line modeling the numbers of childrens and womens bicycles sold\nd. all three lines will give equally reliable predictions.

Answer

Explanation:

Step1: Recall correlation - coefficient concept

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

Step2: Compare given correlation coefficients

We have (r_1 = 0.791) (for men's and women's bicycles), (r_2=0.564) (for men's and children's bicycles), and (r_3 = 0.945) (for children's and women's bicycles).

Step3: Determine the most reliable line

Since (0.945>0.791>0.564), the line with the correlation coefficient of (0.945) (the line modeling the numbers of children's and women's bicycles sold) is the most reliable for prediction.

Answer:

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