Lesson 106 — Multiple regression

Regression: $$ (price in R$ thousand, area m², bedrooms, floor). Interpret each coefficient.

Using $$, calculate the prediction and residual for an 80 m², 3-bedroom, 5th-floor apartment with an observed price of R$ 450 thousand.

$$, $$ predictors, $$, $$. Calculate $$ and $$.

$$. Three models with $$ predictors and $$. Calculate $$ for each and point out the preferable one.

$$, $$, $$, $$. Build the ANOVA table and test the model at the 5% level.

Auxiliary regressions for 3 predictors: $$, $$, $$. Calculate VIFs and identify severe multicollinearity.

Regression of ENEM score on family income ($$) and participation in a tutoring program ($$: 1=yes, 0=no): $$, $$. Interpret $$.

$$, $$, $$, $$. Test $$ at the 5% level (two-tailed).

$$, $$, $$, $$. Construct 95% CI for $$. Use $$.

Four of the five residuals of a regression are: $$. What is the fifth residual?

Which statement about $$ and adjusted $$ is CORRECT?

What is the main practical effect of multicollinearity in multiple regression?

Which statement about partial coefficients in multiple regression is CORRECT?

Regression of monthly family expenditure (R$ thousand) on 4 socioeconomic predictors: $$, $$, $$. Calculate $$, $$, and $$.

Model: $$ (salary in R$ thousand, experience in years, $$=1 if female). Calculate salaries for (a) male, 10 years; (b) female, 10 years. How to include interaction to check if the gap varies with experience?

A researcher has a regression model with 2 predictors ($$, $$) and considers adding a third predictor. Describe two criteria for deciding whether to include it.

Prove that the hat matrix $$ is idempotent: $$.

Data: $$ observations with $$, $$, $$. Write the design matrix $$ and state the procedure to calculate $$ (no need to perform inversion by hand — describe the steps).

Prove that in any regression with an intercept, $$, using the orthogonality $$.

Show that adding a predictor to the model increases $$ if and only if the $$ statistic of the new predictor is greater than 1.