Question 1

A real estate agent uses simple linear regression to predict house prices based on square footage. Which of the following best describes the dependent and independent variables in this scenario?

Accepted Answer

Dependent variable: house price; Independent variable: square footage

Question 2

Which of the following equations represents the simple linear regression model for predicting $$Y$$ from $$X$$?

Accepted Answer

$$Y_i = b_0$ + b_1$ X_i + \varepsilon_i$$

Question 3

In the regression equation $$\hat{Y}_i = b_0$ + b_1$ X_i$$, what does the slope coefficient $$b_1$$ represent?

Accepted Answer

The estimated change in the mean value of $$Y$$ for a one-unit increase in $$X$$

Question 4

A regression analysis yields the equation: $$	ext{house price} = 98.25 + 0.1098 	imes 	ext{(sq.ft.)}. $$What is the predicted price (in $1,000s) for a house with 2,000 square feet?

Accepted Answer

$$317.85$$

Question 5

Which of the following is NOT an assumption of the simple linear regression model?

Accepted Answer

The independent variable $$X is $$normally distributed

Question 6

The coefficient of determination, $$r^2$$, is best interpreted as:

Accepted Answer

The proportion of the total variation in $$Y$$ explained by $$X$$

Question 7

Given the following sums from a regression analysis: $$SSXY = 172,500$$ and $$SSX = 1,571,500$$, what is the value of the slope coefficient $$b_1$$?

Accepted Answer

$$0.1098$$

Question 8

Which formula correctly expresses the total sum of squares ($$SST) in $$terms of explained and unexplained variation?

Accepted Answer

$$SST = SSR + SSE$$

Question 9

A regression model for predicting sales based on advertising expenditure yields $$r^2 = 0.85$. What does this indicate?

Accepted Answer

85% of the variation in sales is explained by advertising expenditure

Question 10

Which of the following is a correct formula for the standard error of estimate ($$S_e) in $$simple linear regression?

Accepted Answer

$$S_e = \sqrt{\dfrac{SSE}{n-2}}$$

Question 11

Which of the following residual plots would indicate a violation of the equal variance (homoscedasticity) assumption?

Accepted Answer

A plot where the spread of residuals increases as $$X$$ increases

Question 12

If the Durbin-Watson statistic $$D is $$much less than 2, what does this suggest about the residuals?

Accepted Answer

There may be positive autocorrelation

Question 13

A t-test for the slope in simple linear regression is used to:

Accepted Answer

Test whether there is a linear relationship between $$X$$ and $$Y$$

Question 14

Which of the following is a correct formula for the confidence interval for the mean value of $$Y$$ given $$X_0$$?

Accepted Answer

$$\hat{Y}_0 \pm t_{\alpha/2} S_e \sqrt{\dfrac{1}{n} + \dfrac{(X_0$ - \bar{X})^2$}{SSX}}$$

Question 15

Which of the following is a potential pitfall when using regression analysis?

Accepted Answer

Extrapolating predictions outside the range of observed $$X$$ values

Question 16

A business analyst finds that the residuals from a regression model show a cyclical pattern over time. What does this indicate?

Accepted Answer

There is autocorrelation in the residuals

Question 17

Which of the following statements about the intercept $$b_0 in a $$regression equation is TRUE?

Accepted Answer

$$b_0 is $$the estimated mean value of $$Y$$ when $$X is $$zero

Question 18

Suppose a regression model is used to predict the price of a car based on its age. The model is $$	ext{price} = 20,000 - 1,500 	imes 	ext{age}. $$What is the predicted price of a 5-year-old car?

Accepted Answer

$$12,500$$

Question 19

Which of the following is the correct formula for the t-statistic to test the significance of the slope $$b_1$$?

Accepted Answer

$$t = \dfrac{b_1$ - \$$beta_1$$}{S_{b_1$}}$$

Question 20

Which of the following best describes the difference between a confidence interval and a prediction interval in regression?

Accepted Answer

A confidence interval estimates the mean value of $$Y$$ for a given $$X$$, while a prediction interval estimates the value of an individual $$Y$$ for a given $$X$$

Chapter 12: Simple Linear Regression – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard