9- A response Y is a function of three independent variables X1 , x , and x 3 that are related as follows questions Y = Bo + P , X , + ( 2 x 2 + B3 X 3 + E. 9.1 Fit this model to the n = 7 data points shown in the accompanying table . X 1 X 2 * 3 US - 3 5 - 1 0 - 2 0 - 1 - 3 O -4 O - 3 -1 3 5 1. 2 Predict Y when X , = 1 , X2 = - 3 , X 3 = - 1. Compare with the observed response in the original data. Why are these two not equal ? 1.3 Do the data present sufficient evidence to indicate that Xz contributes information for the prediction of Y ? ( Test the hypothesis Ho : B , = 0 , using 2 = 0.05 ) 1- 4 Find a 95% confidence interval for the expected value of y, given X , = 1 9 X 2 = - 3 , X 2 = - 11. 5 Find a 95% prediction interval for y, given X , = 1 , X 2 = - 3 , X 2 = - 1 2. The following model was proposted for testing whether there was evidence of salary discrimination against women in a state university system: Y = Bo + B , X , + B 2 x 2 + B3 X , X 2 + BA X 2 + E Where y = annual salary ( in thousands of dollars ) X1 = 1 , if female o , if male X2 = amount of experience ( in years ). When this model was fit to data obtained from the record of 200 faculty members, SSE = 783. 90 , The reduce model 4 = Bo + B ,x 2 + B 2 x , + was also fit and produced a value of SSE = 795 . 23 . 2 . Do the data provide suffient evidence to support the claim that the mean salary depends on the gender of faculty members ? 1 Use 2 = 0.05