Question

In a study of about 1,000 families, the following descriptive statistics were found: mean height of husband = 68 inches, standard deviation = 15, min = 56, max = 83 mean height of wife = 63 inches, standard deviation = 15, min = 53, max = 73 correlation coefficient = 0.25 You are interested in predicting the height of the wife from the height of her husband.

A. Compute the slope of the regression line.

B. Compute the value for the intercept, and provide a sentence that interprets the value.

C. Write the equation of the regression line for this data.

D. Use this information to predict the height of a wife when the height of her husband is 64 inches (include the RMSE).

You don't have to show your work but include your answer for each step.

Answer 1

husband :

mean_h = 68 inches

standard deviation, mean_h = 15 inches

min_h = 56 inches

max_h = 83 inches

wife

mean_w = 63 inches

standard deviation, mean_w = 15 inches

min_w = 53 inches

max_w = 73 inches

correlation coefficient, r = 0.25

A) Slope of regression line in terms of correlation is given by : r*( sd_y / sd_x ) ( because predicting the height of the wife from the height of her husband )

beta_ 1= r*( sd_w / sd_h ) = 0.25*(15/15) = 0.25

B) Intercept = mean_w - mean_h*beta_1 = 63 - 0.25*68 = 63 - 17 = 46

intercept ( 46 inches ) is the value which will be there for Wife's height even if the independent variable ( height of husband ) is 0

C) Equation of line : Height of wife = 46 + 0.25*( height of husband )

D) given height of husband = 64 inches

Height of wife = 46 + 0.25*( height of husband )

Height of wife = 46 + 0.25*64 = 46 + 16 = 62 inches