In today’s Lab you will gain practice with the following concepts from today’s class:

- Interpreting linear regression coefficients of numeric covariates
- Interpreting linear regression coefficients of categorical variables
- Applying the “2 standard error rule” to construct approximate 95% confidence intervals for regression coefficients
- Using the
`confint`

command to construct confidence intervals for regression coefficients- Using
`pairs`

plots to diagnose collinearity- Using the
`update`

command to update a linear regression model object- Diagnosing violations of linear model assumptions using
`plot`

We’ll begin by loading some packages.

`library(tidyverse)`

`## ── Attaching packages ──────────────────────────────────────────────────────── tidyverse 1.2.1 ──`

```
## ✔ ggplot2 3.3.2 ✔ purrr 0.3.3
## ✔ tibble 2.1.3 ✔ dplyr 0.8.3
## ✔ tidyr 1.0.0 ✔ stringr 1.4.0
## ✔ readr 1.3.1 ✔ forcats 0.4.0
```

`## Warning: package 'ggplot2' was built under R version 3.6.2`

```
## ── Conflicts ─────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
```

```
library(knitr)
Cars93 <- as_tibble(MASS::Cars93)
# If you want to experiment with the ggpairs command,
# you'll want to run the following code:
# install.packages("GGally")
# library(GGally)
```

**(a)** Use the `lm()`

function to regress Price on: EngineSize, Origin, MPG.highway, MPG.city and Horsepower.

`# Edit me`

**(b)** Use the `kable()`

command to produce a nicely formatted coefficients table. Ensure that values are rounded to an appropriate number of decimal places.

`# Edit me`

Replace this text with your answer.

**(c)** Interpret the coefficient of `Originnon-USA`

. Is it statistically significant?

`# Edit me`

Replace this text with your answer.

**(d)** Interpret the coefficient of `MPG.highway`

. Is it statistically significant?

`# Edit me`

Replace this text with your answer.

**(d)** Use the “2 standard error rule” to construct an approximate 95% confidence interval for the coefficient of `MPG.highway`

. Compare this to the 95% CI obtained by using the `confint`

command.

`# Edit me`

Replace this text with your answer.

**(e)** Run the `pairs`

command on the following set of variables: EngineSize, MPG.highway, MPG.city and Horsepower. Display correlations in the Do you observe any collinearities?

```
panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...)
{
usr <- par("usr"); on.exit(par(usr))
par(usr = c(0, 1, 0, 1))
r <- abs(cor(x, y))
txt <- format(c(r, 0.123456789), digits = digits)[1]
txt <- paste0(prefix, txt)
if(missing(cex.cor)) cex.cor <- 0.4/strwidth(txt)
text(0.5, 0.5, txt, cex = pmax(1, cex.cor * r))
}
# Edit me
```

Replace this text with your answer.

**(f)** Use the `update`

command to update your regression model to exclude `EngineSize`

and `MPG.city`

. Display the resulting coefficients table nicely using the `kable()`

command.

`# Edit me`

**(g)** Does the coefficient of `MPG.highway`

change much from the original model? Calculate a 95% confidence interval and compare your answer to part (d). Does the CI change much from before? Explain.

`# Edit me`

Replace this text with your answer.

**(h)** Run the `plot`

command on the linear model you constructed in part (f). Do you notice any issues?

`# Edit me`

Replace this text with your answer.