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 $R2\mathrm { R } ^ { 2 }$ = 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

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

R2\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.

Tachinique VanHolt · Accepted Answer

Final Answer : B, Explanation :   The coefficient of determination (  R 2 R^2 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 R^2 R 2   gives the correlation coefficient   r r r  , which is   0.19 ≈ 0.436 \sqrt{0.19} \approx 0.436 0.19 ​ ≈ 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.

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