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.


The professor fit a first-order model to the data that he intends to use to predict a student 's grade on the first test using that student's grades on the first three quizzes.
Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } } :$ at least one $\beta _ { i } \neq 0$ . Use $\alpha = , 05$ . Interpret the result.