A random sample of 150 yachts sold in Canada last year was taken.A regression to predict the price (in thousands of dollars)from length (in metres)has an $\mathrm { R } ^ { 2 } = 18.3 \%$ What is correlation between length and price?
A)0.428
B)0.033
C)0.667
D)0.904
E)0.183

Question

Quizplus · Accepted Answer

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. Its value ranges from -1 to +1, where -1 indicates a strong negative relationship, +1 indicates a strong positive relationship, and 0 means no linear relationship.

In this case, the regression analysis is used to predict the price of a yacht based on its length, so it makes sense to calculate the correlation between length and price.

The correlation coefficient is given by r = sqrt(R-squared), where R-squared is the coefficient of determination from the regression analysis. In this case, R-squared is equal to 0.183, so r = sqrt(0.183) = 0.428.

Therefore, the answer is A) 0.428.

A Random Sample of 150 Yachts Sold in Canada Last R2=18.3%\mathrm { R } ^ { 2 } = 18.3 \%R2=18.3%

A Random Sample of 150 Yachts Sold in Canada Last $\mathrm { R } ^ { 2 } = 18.3 \%$