01.02 Evaluating regression model fit and interpreting model results

Question 1

What is ANOVA tables

Answer 1

Statistical procedure that decomposes the total variation in the dependent variable into the explained and unexplained components to evaluate

Regression is explained component of the variation, while error is the unexplained component

Question 2

What is the Coefficient of determination, R2

Answer 2

R2 evaluates the overall effectiveness of the entire set of independent variables in explaining the dependent variable

% of the variation in the dependent variable that is collectively explained by all the independent variable

Question 3

What are the issues with R2?

Answer 3

R2 always increases as more independent variables are added to the model, even when the marginal contribution of new variables are not statistically significant

High R2 may reflect the impact of a large set of independent variables, rather than how efficiently the set explains the dependent variable - may result in overestimating or overfitting the regression model

Question 4

What is R2a

Answer 4

tool used to overcome the issues with R2

R2a may increase or decrease as more independent variables are added – resolves the overfitting issue

If a new variable only has a small effect on R2, the value of R2a will decrease

Not indicative of the quality of the model fit, nor does it indicate the statistical significance of the slope coefficients

Question 5

What is AIC?

Answer 5

Akaike’s information criterion (AIC)

AIC used if the goal is to have a better forecast

lower the value the better

Question 6

What is BIC?

Answer 6

Schwarz’s Bayesian information criteria (BIC)

BIC is used if the goal is a better goodness of fit

Lower the value, the better the model

Question 7

What are F-tests?

Answer 7

Formal F-test can be used to evaluate nested model

Nested models are such that one model has a higher number of independent variables (full model/ unrestricted model) while another model (restricted model) has only a subset of the independent variable

Question 8

What is the F-statistic used to evaluate H0=b2=b3=0 and Ha:B2 or B3 not equal 0

Answer 8

F-tests evaluate whether the relative decrease in SSE due to the inclusion of Q additional variables is statistically justified

Individual slope coefficients can be tested using t-tests by F-tests provides more meaningful evaluation of the explanatory power of alternative models

F test evaluates the overall model fit – tests whether at least one of the independent variables explains a significant portion of a variation of the dependent variables

Question 9

What is the F-statistic used to evaluate 3 variables H0=b1=b2=b3=0 and Ha:BJ not equal 0

Answer 9

• F test evaluates the overall model fit – tests whether at least one of the independent variables explains a significant portion of a variation of the dependent variables

Question 10

What is predicting the dependent variable?

Answer 10

Regression equation used to make predictions about the dependent variable based on forecasted values of the independent variables

Requires more than one independent variable

Uses estimated intercept and estimated slope coefficients regardless of whether the estimated coefficients are statistically significant different from Zero