LRM_final_1227.pdf - Linear Regression Models Final Exam If...

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Linear Regression Models Final Exam December 21 2020 If you have any questions, please email to [email protected] and/or [email protected] 1. (20 points) The following regression output was obtained using the city-economy data set. Recall that for each of 366 cities in the US, this records the city’s per-capita gross metropoli- tan product, in dollars per person per year, and its population. x = log10(pop) y = pcgmp out = lm(y ~ x) summary(out) ### log10 computes log to the base 10. For example, log10(100) = 2. ## ## Call: ## lm(formula = y ~ x) ## ## Residuals: ## Min 1Q Median 3Q Max ## -21572 -4765 -1016 3686 40207 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -23306 4957 -4.7 3.7e-06 ## x 10246 900 11.4 < 2e-16 ## ## Residual standard error: 7930 on 364 degrees of freedom ## Multiple R-squared: 0.263,Adjusted R-squared: 0.26 ## F-statistic: 130 on 1 and 364 DF, p-value: <2e-16 For the following questions, explain clearly which parts of the output are the basis for your answers. 1.1. (4 points) What is the predictor variable? What is the response variable? Which variables were transformed, and how? 1
1.2. (3 points) Write the equation for the estimated conditional mean function; use numer- ical values rather than symbols like b β 0 . 1.3. (3 points) According to the estimated model, what is the average per-capita gross metropolitan product of cities with a population of one million people? Of cities with a population of two hundred thousand people? Do these numbers seem reasonable? 1.4. (2 points) Based on the estimated coefficients, can you give an estimate of E [ Y | X = 0]?

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