A Statistics Professor Gave Three Quizzes Leading Up to the First

Essay

A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.

$\begin{array}{ccccc}\text { Student}& \text { TestGrade}& \text {Quiz 1 } & \text { Quiz 2 } & \text { Quiz 3 } \\\hline 1 & 75 & 8 & 9 & 5 \\2 & 89 & 10 & 7 & 6 \\3 & 73 & 9 & 8 & 7 \\4 & 91 & 8 & 7 & 10 \\5 & 64 & 9 & 6 & 6 \\6 & 78 & 8 & 7 & 6 \\7 & 83 & 10 & 8 & 7 \\8 & 71 & 9 & 4 & 6 \\ \hline\end{array}$
The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first threequizzes.
a. Identify the dependent and independent variables for the model.
b. What is the least squares prediction equation?
c. Find the SSE and the estimator of $\sigma ^ { 2 }$ for the model.