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.

1. Compute the slope of the regression line.
2. Compute the value for the intercept, and provide a sentence that interprets the value.
3. Write the equation of the regression line for this data.
4. 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

given:
mean_x=   68
mean_y =   63
Sx =   15
Sy =   15
r=    0.25
  
a)  
slope, b = r*Sy/Sx  
b =    =0.25*15/15
b =    0.25
with 1 inch increase in height of husband, the height of wife is increased by 0.25 inches  
  
b)  
intercept, a = ybar - b*xbar  
a =    =63-0.25*68
a =    46
the initial value of height of wife is 46 inches when height of husband is 0.   
this has no practical significance  
  
c)  
height_wife = 46 + 0.25*height_husband  
  
d)  
when x= 64  
yhat =    =46+0.25*64
yhat =    62
  
error = Y - yhat  
error =    =62-60
error =    2
error^2 =    4
RMSE = sqrt(error^2/(n))   2