Question 1

Which of the following is a requirement for inference on the least-squares regression model?

Accepted Answer

The mean of the response variable depends linearly on the explanatory variable.

Question 2

Given the least-squares regression equation $$ \hat{y} = 1.399x + 151.357 $$, what does the slope represent in the context of predicting cholesterol from age?

Accepted Answer

The average increase in cholesterol for each additional year of age.

Question 3

What does a coefficient of determination $$ R^2$ = 0.515 $$ indicate about the regression model?

Accepted Answer

51.5% of the variation in the response variable is explained by the regression model.

Question 4

Which formula is used to compute the standard error of the estimate in least-squares regression?

Accepted Answer

$$ s_e = \sqrt{ \frac{ \sum (y_i - \hat{y}_i)^2$ }{ n - 2 } } $$

Question 5

A large value of $$ \sigma  in $$the regression model indicates:

Accepted Answer

The data are widely dispersed about the regression line.

Question 6

Which of the following is NOT a requirement for testing the significance of the least-squares regression model?

Accepted Answer

The explanatory variable must be normally distributed.

Question 7

When conducting a hypothesis test for the slope $$ \$$beta_1$$  of a $$regression line, which test statistic is used?

Accepted Answer

$$ t = \frac{ b_1$ - \$$beta_1$$ }{ s_{b_1$} } $$

Question 8

If the p-value for the test of the slope in a regression model is less than $$ \alpha $$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence of a linear relationship.

Question 9

Why is it important to check a residual plot before testing $$ H_0$: \$$beta_1$$ = 0 $$?

Accepted Answer

To verify that a linear model is appropriate for the data.

Question 10

In the context of the cholesterol and age example, what does the intercept $$ 151.357 $$ represent in the regression equation $$ \hat{y} = 1.399x + 151.357 $$?

Accepted Answer

The predicted cholesterol level for a female of age zero.

Question 11

Which of the following best describes the meaning of the residual in a regression analysis?

Accepted Answer

The difference between the observed value and the predicted value.

Question 12

Suppose the sum of squared residuals for a regression model is $$ 453.705 $$ and the sample size is $$ 14 . $$What is the standard error of the estimate?

Accepted Answer

$$ s_e = \sqrt{ \frac{ 453.705 }{ 14 - 2 } } = 6.13 $$

Question 13

Which of the following is the correct null hypothesis for a two-tailed test of the regression slope?

Accepted Answer

$$ H_0$: \$$beta_1$$ = 0 $$

Question 14

If the residuals from a regression model are not normally distributed, what is the implication for inference?

Accepted Answer

Inference on the regression model may not be valid.

Question 15

Which of the following steps is NOT part of the classical approach for hypothesis testing of the regression slope?

Accepted Answer

Calculate the p-value using a statistical spreadsheet.

Question 16

A doctor wants to test if there is a linear relationship between age and cholesterol at $$ \alpha = 0.05 . $$Which of the following is the correct alternative hypothesis for a two-tailed test?

Accepted Answer

$$ H_1$: \$$beta_1$$ 
eq 0 $$

Question 17

Which of the following best describes the meaning of $$ \hat{y}_i  in $$the least-squares regression model?

Accepted Answer

The predicted value of the response variable for the $$ith $$individual.

Question 18

Which of the following is true about the standard error of the estimate in regression?

Accepted Answer

It measures the average distance that the observed values fall from the regression line.

Inference on the Least-Squares Regression Model and Multiple Regression

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