Question 1
The table below shows data for
n = 20 observations.
| a. | Use a first-order regression model to find a least squares prediction equation for the model. |
b.
Find a 95% confidence interval for the coefficient of
x1 in your model. Interpret the result.
c.
Find a 95% confidence interval for the coefficient of
x2 in your model. Interpret the result.
d.
Find
R2 and
Ra2 and interpret these values.
e.
Test the null hypothesis
H0:
β1 =
β2 = 0 against the alternative hypothesis
Ha: at least one
βi ≠ 0. Use
Interpret the result.
Question 2
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
H0:
β1 =
β2 =
β3 = 0 against the alternative hypothesis
Ha: at least one
βi ≠ 0. Use
Interpret the result.
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