**Learning Goal: **I’m working on a micro economics question and need an explanation and answer to help me learn.

R – Transformations, units, and elasticity

1. In this exercise you will transform variables, check the effect of changes in units, and calculate the elasticity. Use the Galtonf.csv file for the data for this assignment. You can find it on our canvas site, under files, data, R exercise 4. The Galton data holds an important historical place in the development of statistics and it was the analysis of this data that gave rise to term regression. I’ve put the paper on our canvas site, under Hand outs. It has the title “Regression towards Mediocrity in Hereditary Stature”. The data in Galtonf contains the data for daughters. There is also a codebook with the variable descriptions.

2. Load Galtonf.csv into R as a data frame. I named my R data frame d_galtonf.

3. Run a regression of height on mother. This regression will be the benchmark. I called mine r_1.

4. View your result in a stargazer regression table.

5. The data in d_galtonf is in inches. The first transformation is to transform inches into feet. The code is

d_galtonf$heightf <- d_galtonf$height/12

The first term in the code tells R to create a new variable in the data frame d_galtonf and call it height; and the new variable is defined as the height variable in d_galtonf divided by 12.

6. Now run a regression changing the y variable from height to heightf. I called mine r_2 Before you look at your result, calculate what the new estimates of b_{0} and b_{1 }will be.

7. Create a stargazer table that displays both regressions. The code is

stargazer(r_1, r_2, type=”text”)

8. What your expectation of the change in estimates correct?

9. Now transform the x variable, mother, into into inches. I called the new variable mother. The code is

d_galtonf$motherf <-d_galtonf$mother/12

10. Now run a regression changing the x variable from mother to motherf. I called mine r_3. Before you look at your result, calculate what the new estimates of b_{0} and b_{1 }will be.

11. Create a stargazer table that displays all three regressions. The code is

stargazer(r_1, r_2, r_3, type=”text”)

12. Now transform both the y variable and the x variable into natural logarithms. I called my transformed mother variable lmother. The code for mother is

d_galtonf$lmother <- log(d_galtonf$mother)

13. Run the regression of the log of height on the log of mother.

14. What is the interpretation of the estimate of b_{1}?

15. To make a calculation using regression results and summary stats requires installing a new package called broom. The code is

install.packages(“broom”)

library(broom)

Remember to “comment” out the install.packages once you have installed broom.

16. Now calculate the elasticity of daughter’s height with respect to mother’s height at the means. The first step is to create a “tidy” set of results for the first regression, r_1 (regression output). The code is

results <-tidy(r_1)

17. Next we name the estimate of the coefficient on mother in results. The code is

beta1hat<-results$estimate[2]

18. We now calculate the elasticity at the mean. The code is

elasticity <-mean(d_galtonf$mother)*beta1 hat/mean(d_galtonf$height)

To see the elasticity the code is

elasticity

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