Linear Regression

Question 1

What does simple linear regression explain?

Answer 1

The variation in a dependent variable using the variation in a single independent variable.

Question 2

What is the fitted simple linear regression equation?

Answer 2

Ŷi = b0 + b1Xi.

Question 3

What is the population simple linear regression model?

Answer 3

Yi = b0 + b1Xi + εi.

Question 4

What does the intercept term represent in simple linear regression?

Answer 4

The value of Y when X = 0.

Question 5

What does the slope coefficient represent in simple linear regression?

Answer 5

The change in Y for a one-unit change in X.

Question 6

What is the least squares criterion?

Answer 6

Choose the regression line that minimizes the sum of squared differences between actual and predicted Y values.

Question 7

What is a residual in regression?

Answer 7

The difference between the actual value of Y and the predicted value of Y.

Question 8

What are the main assumptions of simple linear regression?

Answer 8

Linear relationship between X and Y, constant variance of residuals, no correlation among residuals, and normally distributed residuals.

Question 9

What is heteroskedasticity?

Answer 9

A violation of the assumption that the variance of residuals is constant.

Question 10

What is autocorrelation?

Answer 10

A violation of the assumption that residuals are uncorrelated with one another.

Question 11

How is the correlation coefficient defined?

Answer 11

rXY = Cov(X,Y) / (σX × σY).

Question 12

What is the relationship among SST, SSR, and SSE?

Answer 12

SST = SSR + SSE.

Question 13

What does SST measure?

Answer 13

Total Sum of Squares. The total variation in the dependent variable around its mean.

Question 14

What does SSR measure?

Answer 14

Regression Sum of Squares. The variation in Y explained by the regression.

Question 15

What does SSE measure?

Answer 15

Sum of Squared Errors. The unexplained variation in Y, or the sum of squared residuals.

Question 16

What is MSE?

Answer 16

Mean Squared Error. MSE = SSE / (n - 2).

Question 17

What is SEE?

Answer 17

SEE = sqrt(MSE), the standard error of estimate.

Question 18

What does R² measure?

Answer 18

The percentage of total variation in the dependent variable explained by variation in the independent variable.

Question 19

In simple linear regression, how else can R² be calculated?

Answer 19

As r², the square of the correlation coefficient.

Question 20

What is the F-statistic in simple linear regression?

Answer 20

F = MSR / MSE, where for simple linear regression MSR = SSR.

Question 21

What is the null hypothesis for testing the significance of the slope coefficient?

Answer 21

H0: b1 = 0.

Question 22

What are the degrees of freedom for the t-test on the slope coefficient?

Answer 22

n - 2.

Question 23

What does it mean if the slope coefficient is significantly different from zero?

Answer 23

The independent variable has explanatory power for the dependent variable.

Question 24

What is the form of a prediction interval for a forecast?

Answer 24

Ŷ ± tc × sf.

Question 25

What is tc in a prediction interval?

Answer 25

The two-tailed critical t-value with n - 2 degrees of freedom.

Question 26

What is sf in a prediction interval?

Answer 26

The standard error of the forecast.

Question 27

What is the log-lin model?

Answer 27

ln(Yi) = b0 + b1Xi + εi.

Question 28

What is the lin-log model?

Answer 28

Yi = b0 + b1ln(Xi) + εi.

Question 29

What is the log-log model?

Answer 29

ln(Yi) = b0 + b1ln(Xi) + εi.

Question 30

What is the null hypothesis for testing the intercept?

Answer 30

H0: b0 = 0

Question 31

What are the degrees of freedom for a t-test of the intercept?

Answer 31

n - 2.

Question 32

What is an indicator (dummy) variable?

Answer 32

A variable that takes the value 0 or 1 to represent a state.

Question 33

In a regression with a dummy variable, what does the slope coefficient measure?

Answer 33

The sensitivity of Y to a change in state represented by the dummy variable.