# Introduction

The data are a sample of 500 observations in a study where air pollution at a road is related to traffic volume and meteorological variables. All data was collected by the Norwegian Public Roads Administration.

# Getting started

Clone your assignment repo into RStudio Cloud and open the R Markdown file. Don’t forget to load in the necessary packages and configure git.

library(tidyverse)
library(infer)
library(broom)
library(usethis)
use_git_config(user.name="your name", user.email="your email")

If you would like your git password cached for a week for this project, type the following in the Terminal:

git config --global credential.helper 'cache --timeout 604800'

You will need to enter your GitHub username and password one more time after caching the password.This is only good for this single RStudio Cloud project; you will need to cache your credentials for each project you create.

# Data

The response variable (column 1) consist of hourly values of the logarithm of the concentration of $$\mbox{NO}_2$$ (particles), measured at Alnabru in Oslo, Norway. The predictor variables (columns 2 to 8) are the logarithm of the number of cars per hour, temperature 2 meter above ground (degree C), wind speed (meters/second), the temperature difference between 25 and 2 meters above ground (degree C), wind direction (degrees between 0 and 360), hour of day and day number from October 1, 2001.

StatLib—Datasets Archive. (2020). Lib.stat.cmu.edu. Retrieved 7 April 2020, from http://lib.stat.cmu.edu/datasets/

no <- read_delim(file = "http://lib.stat.cmu.edu/datasets/NO2.dat",
delim = "\t", col_names = FALSE)

# Set a seed

Before you get started, set the seed so each person in your group will be able to reproduce your analysis.

set.seed(8675309)

# Exercises

In addition to the linear model fitting functions, statistical distribution functions, and base R arithmetic functions, your code should only contain functions from the loaded R packages above unless explicitly stated in an Exercise.

## Data cleaning and exploration

1. Fix the column names in no to something meaningful.

2. Create a well-polished visualization that investigates the relationship between log concentration of $$\mbox{NO}_2$$ and the hour of the day.

3. Comment on what you observe from your visualization in Exercise 2.

## CLT-based inference

1. Create a 95% confidence interval for the mean log concentration of $$\mbox{NO}_2$$. What assumptions must hold for this interval estimate to be valid?

2. Let $$\mu$$ be the mean number of cars per hour that travel on Alnabru in Oslo, Norway. Suppose the average number of cars per hour that travel on similar roads is known to be 2000. Is the sample data in no strong enough evidence at the $$\alpha = .05$$ level to suggest that the road in Alnabru is less traveled?

3. Assume all population parameters are unknown. In a general hypothesis testing framework, what is the smallest observed test statistic value, $$\frac{\bar{x} - \mu_0}{s / \sqrt{n}}$$, we could obtain and still reject the null hypothesis at the $$\alpha = 0.01$$ significance level when $$H_A: \mu > \mu_0$$ and $$n=32$$. Here quantity $$\mu_0$$ represents the value of $$\mu$$ under the null hypothesis.

4. If you reject the null hypothesis at the $$\alpha = 0.02$$ significance level, then you will also reject the null hypothesis at the $$\alpha = 0.01$$ significance level. Explain in detail, or with an example, why this claim is true or false.

## Regression inference

1. Consider a linear model with log concentration of $$\mbox{NO}_2$$ as the response and temperature 2 meter above ground (degree C) as the single predictor. Compare the simulation-based inference 90% confidence interval for the slope and the 90% confidence interval for the slope derived from the regression output. You may assume the linear regression conditions hold without verifying via plot diagnostics.

2. Perform backwards elimination with AIC as the selection criteria, where the full model consists of predictors in columns 2 through 7 of no and the response is log concentration of $$\mbox{NO}_2$$. Display the model terms, estimates and p-values in a tidy format. Hint: sort the data chronologically before model fitting, it will make things easier in Exercise 10.

3. Check if all the linear model conditions are satisfied for the final model from Exercise 9.

4. Compute 95% confidence intervals for two coefficients in your final model from Exercise 9. Provide an interpretation for these intervals.

# Submission

Knit to PDF to create a PDF document. Stage and commit all remaining changes, and push your work to GitHub. Make sure all files are updated on your GitHub repo.

Please only upload your PDF document to Gradescope. Associate the “Overall” graded section with the first page of your PDF, and mark where each answer is to the exercises. If any answer spans multiple pages, then mark all pages.

Only one team member needs to submit for the group. After you hit submit, go to View or edit group and select all your team members from the drop-down menu.