It turns out that the 300 students surveyed were evenly divi

It turns out that the 300 students surveyed were evenly divided amongst first-, second- and third-year undergraduates. A scatterplot with points colour-coded by student level and regression lines from a full ANCOVA model using hours/week studying and student level as the predictors, as well as a residual plot from this full ANCOVA. are given below: The coefficients summary table for the full ANCOVA modal [third-year students used as the base] is: What values go in the cells marked (1), (2), (3) and (4) in the ANOVA table? (2 marks) What vallue goes in the cell marked (5) in the ANOVA table? (1 mark) Is the full ANOVA modal needed, or can we plausibly use a parallel ANOVA? (1 MARK) Test whether there is a statistically significant difference between the slopes for second-year and third-year students. (1 mark) Find a 99percent confidence interval for the difference in intercepts between first- and third-year students. (1 mark) Based on the residual plot, are there any issues with the underlying assumptions of the ANCOVA modal? (1 MARK) Consider a linear regression of response variable Y = (Y1,...,YN) on a predictor variable X = ( X1,.....,xn).= (Xi,...X). The least-squares estimates of intercept and slope, a and bete arc the values minimizing the function: d(a,beta) =^n segma i=1 {Yi-(a+ betaXi)}^2 Further, predicted values are y(x) = a = betax. Find y(x), where x is the average of the x,s. (2 mark)

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