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 feet)has an $\mathrm { R } ^ { 2 }$ = 19.00%.What would you predict about the price of the yacht whose length was one standard deviation above the mean?
A)The price should be 1 SD above the mean in price.
B)The price should be 0.436 SDs above the mean in price.
C)The price should be 1 SD below the mean in price.
D)The price should be 0.900 SDs above the mean in price.
E)The price should be 0.872 SDs above the mean in price.

Question

Quizplus · Accepted Answer

The coefficient of determination ($R^2$) is 19.00%, or 0.19, which means that 19% of the variance in the yacht prices can be explained by the length of the yacht. The square root of $R^2$ gives the correlation coefficient $r$, which is $\sqrt{0.19} \approx 0.436$. This implies that a 1 standard deviation increase in length is associated with a 0.436 standard deviation increase in price, making choice B correct.

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

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