A Statistics Professor Gave Three Quizzes Leading Up to the First

question 66

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.

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Definitions:

Liver Cancer

A disease characterized by malignant cells forming in the tissues of the liver, which can be primary or secondary (metastatic).

Liver Failure

A critical condition where the liver loses its function, which can lead to life-threatening complications.

Fungal Infection

A disease condition caused by the growth of fungi in or on the body, leading to symptoms like itching, rashes, or more severe systemic issues.

Contagious

Having a disease that can easily be transmitted to others.