Suppose the correlation between heights of fathers and the heights of their (adu

Question

Suppose the correlation between heights of fathers and the heights of their (adult) sons is r = 0.54. All heights are measured in inches

Which if the following is true?
Incorrect nothing can be concluded unless one knows the regression equation form.
Incorrect sons are, on the average, taller than their fathers.
Incorrect 54% of all sons are taller than their fathers.
Correct: taller-than-average fathers tend to have taller-than-average sons.
Incorrect taller-than-average fathers tend to have shorter-than-average sons.

If both fathers' and sons' heights are measured in centimeters (1 inch = 2.54 cm), then the value of the new correlation coefficient will be:
0.54
0.54/2.54
0.54×2.54
0.54×2.54×2.54
0.54/(2.54×2.54)

What percentage of total sample variation in sons' heights will be explained by fathers' height?

Explanation / Answer

Correlation coefficient doesn't depend on scale change so the new correlation coefficient will also bw 0.54.

Option A is correct.

Percentage of sample variation in son's height that will be explained by father's height

= 0.542

= 0.2916

= 29.16%

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