Question 5. In this question we consider the regression of a response variable Y on predictors X1, X2, and X3, based on n=100 observations. (a) OUTPUT#1 on page 3 gives parts of the 'R' output for the least squares t A Y = b0 + b1X1+ b2X2 + b3X3. It. also gives a number of residual plots. 8.6) [1.5 points} Briey comment on each residual plot. Do you see any violations of the model assumptions? Explain. ai) [1.5 points] Test Ha : ,81 = 52 = ,83 = 0 against H : Not H0, at 1% signicance level, E state an}r assumptions that you need for this test. > R2=Im(Y~X1+)2+*3) > summary(R2) Coefficients: Estimate Std. Error tvalue Pr(> It) (Intercept) 2.0533 0.3561 5.766 9.83e-08 X1 0.6894 0.2989 2.306 0.0232 X2 1.9092 0.2582 7.394 X3 0.2577 0.2137 1.206 5.31e-11 0.2308 Residual standard error: 1.547 on 96 degrees of freedom Multiple R-Squared: 0.7137. F-statistic: 79.78 on 3 and 96 DF, p-value: