--- title: "Lab 10" author: "Your Name Here" date: "" output: html_document --- ##### Remember to change the `author: ` field on this Rmd file to your own name. ### Learning objectives > 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. ```{r} library(tidyverse) 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) ``` ### Linear regression with Cars93 data **(a)** Use the `lm()` function to regress Price on: EngineSize, Origin, MPG.highway, MPG.city and Horsepower. ```{r} # 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. ```{r} # Edit me ``` > Replace this text with your answer. **(c)** Interpret the coefficient of `Originnon-USA`. Is it statistically significant? ```{r} # Edit me ``` > Replace this text with your answer. **(d)** Interpret the coefficient of `MPG.highway`. Is it statistically significant? ```{r} # 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. ```{r} # 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? ```{r} 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. ```{r} # 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. ```{r} # 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? ```{r, fig.height = 12, fig.width = 12} # Edit me ``` > Replace this text with your answer.