(a) Kebri LTD. sells Radios and Televisions. They have recorded their monthly revenue as follows. Revenue in Ksh '000' (Y) 330 180 209 390 391 304 347 461 538 610 Radio Units (X1) 55 71 92 113 134 156 171 193 219 232 Television Units (X2) 63 120 151 73 42 81 93 103 124 145 (i) Estimate the regression equation of Revenue on Radio units and Television units. (ii) Construct a 98% confidence interval for Revenue if Radio units sold is 300 and Television units sold is 250. (iii) Comment on the significance of the regression model at 1% significance level. (iv) Test at 5% significance level whether Radio sales and Television sales are significant predictors of Revenue. (v) Test for autocorrelation using the Durbin Watson statistic. (Assume DL = 1.25 and DU = 1.7) (b) The following data represents an extract of the final votes, of ten candidates, for an election influenced by previous public service score card of a candidate. Votes 502 685 765 587 728 603 465 625 539 655 Score card 12.5 13.5 13.5 10.5 11.5 9.5 14.5 10.5 11.5 12.5 A survey was done to verify whether voters relied on the previous scored card to make their decision. It was discovered that most of the voters were also interested on whether the candidate was a graduate (G) or a non-graduate (N). With this new information, a new summary was obtained as follows: Votes 515 675 755 585 725 605 495 695 535 645 Score card 13.5 10.5 12.5 11.5 13.5 9.5 10.5 13.5 14.5 12.5 Education G G G N G N N N G G Required: Use the Adjusted-R square to determine whether education level had any influence in the final votes obtained by a candidate (Assume G = 0 and N = 1) (c) Discuss the effects of autocorrelation in regression. List ways in which an analyst can deal with autocorrelation. (d) Discuss the effects of multicollinearity in regression and list ways in which an analyst can deal with multicollinearity. (e) Below is the correlation matrix of the variables Y, X1, X2 and X3. Test for the presence of multicollinearity between X1 and X2, between X1 and X3, and between X2 and X3 if the sample size was n=21. Y X1 X2 X3 Y 1 0.3786 0.8976 0.9878 X1 1 0.8945 0.2167 X2 1 0.7356 X3 1 (f) Explain the meaning of intrinsically linear regression model. (g) Consider the model = + , where a and b are constants and is the error term. Explain how you would estimate parameters a and b