#---
# title: "CSC 171 - Lab 6"
# author: "Student Name"
# output: word_document
#---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

### Instructions

In this lab, you will begin to get oriented with R and work with some data. 

#### How to **complete** this assignment.

* Attempt each exercise in order.

* In each code chunk, if you see "<font color="789922"># INSERT CODE HERE"</font>, then you are expected to add some code to create the intended output (Make sure to erase "# INSERT CODE HERE" and place your code in its place).

* If my instructions say to "Run the code below..." then you do not need to add any code to the chunk. 

* Many exercises may require you to type some text below the code chunk, interpreting the output and answering the questions. 

* Please follow the Davidson Honor Code and rules from the course syllabus regarding seeking help with this assignment.

#### How to **submit** this assignment.

* When you are finished, click the "Knit" button at the top of this panel. If there are no errors, an word file should pop up after a few seconds.

* Take a look at the resulting word file that pops up. Make sure everything looks correct, your name is listed at the top, and that there is no 'junk' code or output. 

* Save the word file (to your local computer, and/or to a cloud location) as: **Lab 6 "Insert Your Name"**.

* Use [this link](https://forms.gle/YsbXtC7ZnWH6fTHB6) to upload your word file to my Google Drive folder. **Do not** upload the original .Rmd version. 

* This assignment is <font color="darkred">**due Thursday, July 21, 2022, no later than 9:30 am Eastern**</font>. Points will be deducted for late submissions. 

* <font color="darkblue">TIP:</font> Start early so that you can troubleshoot any issues with knitting to word. 

#### Grading Rubric

There are 6 possible points on this assignment.

**Baseline (C level work)**

- Your .Rmd file knits to word without errors.
- You answer questions correctly but do not use complete sentences.
- There are typos and 'junk code' throughout the document.
- You do not put much thought or effort into the Reflection answers.

**Average (B level work)**

- You use complete sentences to answer questions. 
- You attempt every exercise/question. 

**Advanced (A level work)**

- Your code is simple and concise.
- Unnecessary messages from R are hidden from being displayed in the word.
- Your document is typo-free.
- At the discretion of the instructor, you give exceptionally thoughtful or insightful responses.

---


#### **Exercise 1. (3 points)** 

In this exercise, you will further analyze the `Wage` data set.

(A) Perform polynomial regression to predict wage using age. Use cross-validation to select the optimal degree d for the polynomial. What degree was chosen, and how does this compare to the results of hypothesis testing using ANOVA? Make a plot of the resulting polynomial fit to the data.

(B) Fit a step function to predict `wage` using `age`, and perform cross-validation to choose the optimal number of cuts. Make a plot of the fit obtained.


```{r}
#insert code here
```

<font color="darkred">**ANSWER:**</font>






#### **Exercise 2. (3 points)** 

This question relates to the `College` data set.

(A) Split the data into a training set and a test set. Using `out-of-state tuition` as the response and the other variables as the predictors, perform forward stepwise selection on the training set in order to identify a satisfactory model that uses just a subset of the predictors.

(B) Fit a GAM on the training data, using `out-of-state tuition` as the response and the features selected in the previous step as the predictors. Plot the results, and explain your findings.

(C) Evaluate the model obtained on the test set, and explain the results obtained.

(D) For which variables, if any, is there evidence of a non-linear relationship with the response?


```{r}
#insert code here
```

<font color="darkred">**ANSWER:**</font>