Quiz guide:

- Know how to compute b1 given correlation and standard deviation of y and standard deviation of x.

- Know the basic relationship of SST = SSR + SSE. Know also that by knowing two of them, you know the third.

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Know how the various ways R-sq is computed.

- Know how to compute yhat if given the fitted model and an x value. Know how to compute the residual: e = y - yhat (notthe other way around).

- Know how to compute SSE from a set of residual values.

- Know how to compute SST from a set of y values.

- For the simple linear regression case, know how to compute MSE given SSE and n.

- Know that testing of Beta1= 0 is the test of relationship or not in a regression context (whether using reported p-value or using confidence interval).

- Know how to compute the t-statistic for testing "Beta1" equalinganyparticular value including for testing "Beta1" equaling 0. Namely, if you are testing Beta1 = Beta1*, then t = (b1- Beta1*)/SE(b1). In the special case of Beta1* = 0, then t = b1/SE(b1).

- Know how to conclude the testing of Beta1 = 0 given output, whether based on a p-value or confidence interval.

- For a given x value, know how to calculate a prediction of y from a simple linear regression output. Nothing more than sticking x in the fitted model. (Note: you should also know how to get predictions from a multiple regression).

- Know the basic ideas of a confidence interval for the mean vs. prediction interval in a regression setting.

-Understand the role of residual analysis in assessing model appropriateness.Know appropriateness of model fit doesNOTcome exclusively from a t-statistic, R-sq, or a p-value.

- Remember we are hoping to see that the residual vs. fitted (predicted) values plot reflect a random pattern with constant variation. If the residuals are funneling, then we have aviolationof the constant variance assumption for the underlying error term (not good!).If the residuals are showing pattern like curvature, then the linear fit is not the best fit. In addition, we need to check the residuals for normality given the assumption of normality for the underlying error term.

- Understand the basic difference between a marginal slope and partial slope. Know that the coefficient in front of an X variable can change in the presence or not of other X variables.

-Know how to compute the overall F statistic if you know SSR, SSE, n, and # of X variables ("K").

- Know how to compute thepartial F test statistic ifyou are given two regression outputs: the larger model (FM) and the smaller model (RM).

- Know the meaning of multicollinearity: namely, the correlation of X variables with other X variables.

- Know the definition of VIF and how to compute a VIF value from provided output.

- Know what happens to SSE, SSR, SST, and R-sq as you add X variables (or take away).

- Be able to plug-in prediction with a multiple regression. Namely, if given a regression output and values of X variables, then be able to stick in the values into the regression model to get a yhat value. Basic calculator computation.

- Recognize that with indicator variables, different categories are accounted for by the 0/1 values. Consider the simple situation of yhat = 10 + 5*Male. Is the category of Female accounted for? Yes it is. Female is accounted for when Male = 0. Female is the intercept (baseline).

- If we had three categories (HS, College, Grad), and ran a regression to get yhat = 10 - 2*HS + 4*College. Is Grad accounted for? Yes, when HS = 0 and College = 0; Graduate is the intercept (baseline).Now, what if we ran another regression on College and Grad but not HS, what would be the intercept? Answer: 8 (Why? Work it out to convince yourself.) What would be the coefficients for College and Grad? Answer: 6 and 2 (Why? Work it out to convince yourself.).

- Know the maximum number of indicator variables that could be allowed into the regression. Remember when we had two genders, we only needed one indicator variable. When we had 3 neighborhoods, we only needed at most 2 neighborhood indicator variables. In general, for "J" categories, we need at most "J - 1" indicator variables.

- If we have yhat = 10 + 2X + 3(X*I), what is the slope coefficient on X when I = 0? Answer: 2 (Why? Work out it out.) What is the slope coefficient on X when I = 1? Answer: 5 (Why? Work it out to convince yourself.)

- Know the interpretation of coefficients from log(Y) and/or log(X) fitted models.

- Know how to make predictions from any type of model presented in last lecture (e.g., indicator, interaction, quadratic, transformed Y and/or X, or a combination). Make sure you are able to return to original units if a log(Y) regression is fit.