2. Suppose the interaction model Y=l30+31x1 "'[323524'1339'13'2i'8 was t to n = 20 data points, and the following results were obtained: > sum( lm( y ~ 1 )$residuals"2 ) [l] 57 > sum( 1m( y ~ x1 )$residuals*2 ) [l] 40 > sum( 1m( y ~ x2 )$residuals"2 ) [l] 45 > sum( 1m( y ~ x1 + x2 )$residuals"2 ) [l] 36 > sum( 1m( y ~ x1 + x2 + I(xl*x2) )$residuals"2 ) [l] 30 > 1m( y ~ :1 + x2 + I(x1*x2) )$coefficients (Intercept) x1 x2 I(x1 * x2) g) l O 5 2 3 Perform the significance of the regression test at 05 = 0.05. Do x1 and x2 interact? Perform the appropriate test at on = 0.05. Would a 95% condence interval for [33 cover zero? Justify your answer. Construct a 90% confidence interval for [33. \"Hint\": You have the value of ['33 and the value of the F test statistic for the test H02B3=0 vs. H1:B30 frompart(b). Is there sufficient evidence to indicate that x2 contributes information for the prediction of y ? Perform the appropriate test at or = 0.05. What is the p-value of this test? Estimate the change in E ( Y) for every l-unit increase in .761, when .762 = 2. Estimate the change in E ( Y) for every lunit increase in x2, when x1 = 3