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.

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 three quizzes.
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.

Question

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.

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 three quizzes.
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.

Quizplus · Accepted Answer

The Answer is a. The dependent variable is "test grade." There are three independent variables: "quiz 1," "quiz 2," and "quiz 3."
b.

\hat { y } = 15.8687 + 2.6796 x _ { 1 } + 1.9780 x _ { 2 } + 3.6967 x _ { 3 }

c.

\mathrm { SSE } = 317.1874

; The estimator of

\sigma ^ { 2 }

is

79.2968

.

A Statistics Professor Gave Three Quizzes Leading Up to the First