Module 10.2: ANOVA and Goodness Of Fit

Question 1

What does ANOVA stand for?

Answer 1

Analysis of variance

Question 2

What does the total sum of squares (SST) measure?

Answer 2

Total variation in the dependent variable

Question 3

SST is equal to the sum of the squared differences between which two values?

Answer 3

Actual Y-values and the mean of Y

Question 4

What does the sum of squares regression (SSR) measure?

Answer 4

Variation in the dependent variable explained by the independent variable

Question 5

What is the mean square regression (MSR) in a simple linear regression?

Answer 5

Equal to SSR

Question 6

What does the sum of squared errors (SSE) measure?

Answer 6

Unexplained variation in the dependent variable

Question 7

SSE is also known as what?

Answer 7

Sum of squared residuals or residual sum of squares

Question 8

How is the mean squared error (MSE) calculated?

Answer 8

SSE divided by degrees of freedom

Question 9

What are the degrees of freedom in a simple linear regression?

Answer 9

n - 2

Question 10

What does the ANOVA table summarize?

Answer 10

Variation in the dependent variable

Question 11

What does the standard error of estimate (SEE) represent?

Answer 11

Standard deviation of residuals

Question 12

What is the coefficient of determination (R^2)?

Answer 12

Percentage of total variation in the dependent variable explained by the independent variable

Question 13

How is R2 calculated?

Answer 13

SSR divided by SST

Question 14

For simple linear regression, how can R2 be computed?

Answer 14

By squaring the correlation coefficient, r

Question 15

What does the F-statistic assess?

Answer 15

How well a set of independent variables, as a group, explains the variation in the dependent variable

Question 16

What is the formula for the F-statistic?

Answer 16

MSR / MSE

Question 17

True or False: The F-test is a one-tailed test.

Answer 17

True

Question 18

What is the decision rule for the F-test?

Answer 18

Reject H0 if F > Fc

Question 19

What does rejecting the null hypothesis in the F-test indicate?

Answer 19

A significant linear relationship between independent and dependent variables

Question 20

What does a t-test in regression test?

Answer 20

The hypothesis that the true slope coefficient, b1, is equal to a hypothesized value

Question 21

What is the decision rule for tests of significance for regression coefficients?

Answer 21

Reject H0 if t > + tcritical or t < -tcritical

Question 22

What is an indicator variable?

Answer 22

A dummy variable that takes on a value of 1 or 0 based on a condition

Question 23

In a regression analysis, how can an indicator variable be used?

Answer 23

To test whether a condition has a significant effect on the dependent variable

Question 24

What does the slope coefficient b1 represent in the context of an indicator variable?

Answer 24

The difference in means of the dependent variable for the two conditions

Question 25

What are the two variables in SSR calculation?

Answer 25

Predicted Y values and the mean of Y.

Question 26

Formula for MSR or mean square regression?

Answer 26

SSR divided by the number of independent variables.