. The 95% CI of a slope coefficient in a multiple regression is narrower, the larger the R-squared of the regression. Why? . The 95% CI of a slope coefficient in a multiple regression is wider, the more the variable is correlated with the other right-hand-side variables. Why? . What's the difference between B in f = a + 3x1 and 51 in yE = Bo + lel + Em? Why is this difference called omitted variable bias? . You want to estimate differences in spending on cigarettes by family income, and you are also interested how this difference in spending varies by the level of education of the adults in the family. Write down a regression that can uncover those differences, and interpret the coefficients of that regression. (Hint: you may define education as a binary variable, high versus low.) . Give an example of a multiple regression with two binary right-hand-side variables and their interaction. Write down the regression and interpret its coefficients. . What's a 37, plot, and what is it good for? Give an example. . You want to predict ywith the help of ten xvariables using multiple linear regression. A regression that includes the ten variables produces an R-squared of 0.4. A regression that includes those ten variables together with many of their interactions has 100 variables altogether, and it produces an R-squared of 0.43. List pros and cons for choosing each of the two regressions for your prediction. . You want to estimate the effect of x on ywith the help of a multiple regression. You have 10 2 variables that you want to condition on to get closer to causality. A regression that includes the ten variables produces a coefficient on xthat is 0.40, SE = 0.05. A regression that includes those 10. 11. 12. 13. 14. 15. ten variables together with many of their interactions gives a coefficient estimate of 0.35 and SE = 0.10. List pros and cons for choosing each of the two regressions for your causal analysis. . True or false? Why? Multiple regression analysis of observational data shows expected differences in the dependent variable corresponding to differences of an explanatory variable, ceteris paribus. In a dataset of a cross-section of cars advertised on an online platform, log price is regressed on a binary variable that is one if the ad comes from a dealer and zero if it comes from the owner of the car. The slope coefficient is 0.1 . When we add the age of the car to the regression, the slope coefficient on the same binary variable is 0.05. Interpret both numbers. In the previous example the coefficient on the age of the car is 0.1. Are dealer-advertised cars older or younger on average? By how much? Log hotel price is regressed on distance to the city center, average customer rating, and number of stars in a linear regression, using data on a cross-section of hotels in a city. The slope coefficient on stars is 0.2. Interpret this number. The standard error on the slope coefficient in the previous question is 0.05. What's its 95% Cl and what does that mean? We are interested in how airline prices are related to the distance traveled and the size of the market (number of passengers). The data consists of average prices on the most popular markets (routes) of the USA (e.g., BostonChicago) for the year 2018. OLS estimates of our regression are the following: (In price)E = 4.4 + 0.3distance 0.06passengers (10.23) where In price is log price, distance is measured in thousand miles, and passengers is the number of passengers per day (thousands). Interpret the two slope coefficient estimates. We include the interaction of distance and passengers in the same regression and get a coefficient estimate of 0.002. Interpret this number. What can we conclude from its inclusion about the interaction of distance and passengers if the SE is 0.002