A statistics class has assignments, two term tests and a nal exam. The instructor wished to see how well the nal exam mark was related to the assignment and term test marks so used least squares to t a linear model to the marks for 20 students. Here is the resulting parameter estimates table.
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -11.87286 8.17407 -1.45 0.1657
test1 1 0.50015 0.08800 5.68 <.0001
test2 1 0.55284 0.13449 4.11 0.0008
assn 1 0.20775 0.12309 1.69 0.1109
a) Give 95% con dence intervals for the parameters of the model.
b) If we are told that the sum of corrected total sum of squares is 2501.09 and the model sum of squares is 2314.13, construct the Analysis of Variance table for the tted model.
c) Estimate the standard deviation of the error terms.
d) Calculate R2 for the tted model and give its interpretation.
e) An alternative model which did not include the second test was tted for which the error sum of squares was 384.40. Calculate the F statistic to compare this reduced model to the full model above and verify that it is equal to the square of the appropriate t test statistic in the full model.