Question

The scatterplot below summarizes husbands and wives heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Summary output of the least squares fit for predicting wife's height from husbands height is also provided in the table.
           Estimate   Std error   T value       Pr(>|t)
Intercept       43.5755       4.6842       9.30       0.0000
height-husband   0.2863       0.0686       4.17       0.0000
In this scenario what is the response variable?

Looking at the graph, is there strong evidence that taller men marry taller women? Explain.

the equation of the regression line for predicting wifes height from husbands height is:
wifes height = 43.5755+0.2863*husbands height.
interpret the slope and intercept in the context of the application.

Given that R^2=0.09, what is the correlation, r, between the heights in the data set?

You meet a married man from Britain who is 5'9" (69 inches) what do you predict his wifes height to be? also how reliable is prediction?

Answer 1

1. The rrsponse variable is the height of the wife.

2. Since no graph has been provided , the interpretation of graph isn't possible.

3. From the regression equation,it can concluded that the wife's height increases by .286 times for an unit increase.in height of her husband added to the intercept term (43.58).

4.Since the p value for both intercept and husband height is 0 that is less than 0.05 , we conclude that the intercept and slope coefficient affects the dependent variable significantly.

5.R^2 =0.09, then r=√R^2=√.09=0.3 , the correlation coefficient between heights is 0.3.

6. If height of husandhis 69 inches,then the height of wife=43.58+0.286(69)= 63.31inches and the fit is not reliable because of the low R^2 value(.09).