The purpose of this in-class lab is to practice conducting hypothesis tests about regression parameters in R. The lab may be completed in a group. To get credit, upload your .R script to the appropriate place on Canvas.

## For starters

Open up a new R script (named ICL7_XYZ.R, where XYZ are your initials) and add the usual “preamble” to the top:

# Add names of group members HERE
library(tidyverse)
library(broom)
library(wooldridge)
library(magrittr)
library(modelsummary)

We’ll use a new data set on Research and Development (R&D) expenditures, called rdchem. The data set contains information on 32 companies in the chemical industry.

df <- as_tibble(rdchem)

Check out what’s in the data by typing

datasummary_df(df)
datasummary_skim(df,histogram=FALSE)

The main variables are measures of R&D, profits, sales, and profits as a percentage of sales (profmarg, i.e. profit margin).

## Regression and Hypothesis Testing

Estimate the following regression model: $rdintens = \beta_0 + \beta_1 \log(sales) + \beta_2 profmarg + u$ Note that the variable $$log(sales)$$ already exists in df as lsales. $$rdintens$$ is in percentage units, so a number of 2.6 means that the company’s total R&D expenditures are 2.6% of its sales.

I won’t show you the code for estimating this model, as it should be old hat by now. If you’ve forgotten, I recommend looking at code from a previous lab.

1. Interpret the coefficient on lsales. If $$sales$$ increase by 10%, what is the estimated percentage point change in $$rdintens$$?
3. Using the output of tidy(est), test the hypothesis that sales affects R&D intensity at the 10% level. In other words, test: $H_0: \beta_1 = 0; H_a: \beta_1 \neq 0$
4. Does your answer to (3) change if you instead consider a one-sided alternative? (i.e. $$H_a: \beta_1 > 0$$)
5. Now consider the $$\beta_2$$ parameter. Is there a statistically significant effect of profit margin on R&D intensity?