A research studied the correlation between physical characteristics of sisters and brothers. Here are data on the heights (in inches) of 11 adult pairs. Brothers are: ( 73, 70, 71, 67, 65, 63, 62, 60, 64, 75, 72 ) Sisters are: ( 72, 69, 59, 68, 54, 66, 52, 58, 57, 62, 64 ) What is the t-statistic for linear regression model whose independent variable is brother heights and dependent variable sister heights. a) Find the correlation and the equation of the least squares line for predicting sister’s height from brother’s height.
b) Carlos is 72 inches tall. Predict the height of his sister.
c) Based on the scatterplot and correlation r, do you expect your prediction to be very accurate? Why?
d) Is there evidence of a significant linear association between physical characteristics of sisters and brothers (a=0.05 level)?
e) What is the meaning of R2 in this example? Describe the meaning of R2 value in this example so that a non-statistician can understand.