LAB 4E: Some Models Have Curves
Lab 4E  Some models have curves
Directions: Follow along with the slides, completing the questions in blue on your computer, and answering the questions in red in your journal.
Making models do yoga

So far, we have only worked with prediction models that fit the line of best fit to the data.

What happens if the true relationship between the data is nonlinear?

In this lab, we will learn about prediction models that fit best fitting curves to data.

Before moving on, load the
movie
data and split it into two sets:– A set named
training
that includes 75% of the data.– And a set named
testing
that includes the remaining 25%.– Remember to use
set.seed
.
Problems with lines

Before learning how to fit curves, let's first fit a linear model for reference.

Train a linear model predicting
audience_rating
based oncritics_rating
for thetraining
data. Assign this model tomovie_linear
. 
Fill in the blanks below to create a scatterplot with
audience_rating
on the yaxis andcritics_rating
on the xaxis using yourtesting
data.xyplot(____ ~ ____, data = ____)

Previously, you used
add_line
to plot the line of best fit. An alternative function for plotting the line of best fit isadd_curve
, which takes the name of the model as an argument. 
Run the code below to add the line of best fit for the
training
data to the plot.add_curve(movie_linear)

Describe, in words, how the line fits the data. Are there any values for
critics_rating
that would make obviously poor predictions?– Hint: how does the linear model perform on very low and very high values of
critics_rating
? 
Compute the MSE of the linear model for the
testing
data and write it down for later.– Hint: refer to lab 4B.
Adding flexibility

You don't need to be a fullfledged Data Scientist to realize that trying to fit a line to curved data is a poor modeling choice.

If our data is curved, we should try to model it with a curve.

Instead of fitting a line, with equation of the form
 we might consider fitting a quadratic curve, with equation of the form
 or even a cubic curve, with equation of the form
 In general, the more coefficients in the model, the more flexible its predictions can be.
Making bendy models

To fit a quadratic model in
R
, we can use thepoly()
function.– Fill in the blanks below to train a quadratic model predicting
audience_rating
fromcritics_rating
, and assign that model tomovie_quad
.movie_quad < lm(____ ~ poly(____, 2), data = training)

What is the role of the number 2 in the
poly()
function?
Comparing lines and curves

Fill in the blanks below to
– create a scatterplot with
audience_rating
on the yaxis andcritics_rating
on the xaxis using yourtesting
data, and– add the line of best fit and best fitting quadratic curve.
– Hint: the
col
argument is added to theadd_curve
functions to help distinguish the two curves.xyplot(____ ~ ____, data = ____) add_curve(____, col = "blue") add_curve(____, col = "red")

Compare how the line of best fit and the quadratic model fit the data. Which do you think has a lower
test
MSE? 
Compute the MSE of the quadratic model for the
test
data and write it down for later. 
Use the difference in each model's
test
MSE to describe why one model fits better than the other.
On your own

Create a model that predicts
audience_rating
using a cubic curve (polynomial with degree3
), and assign this model tomovie_cubic
. 
Create a scatterplot with
audience_rating
on the yaxis andcritics_rating
on the xaxis using yourtest
data. 
Using the names of the three models you have trained, add the line of best fit, best fitting quadratic curve, and best fitting cubic curve for the
training data
to the plot. 
Based on the plot, which model do you think is the best at predicting the
testing
data? 
Use the test MSE to verify which model is the best at predicting the
testing
data.