LAB 4F: Some Models Have Curves

Lab 4F - Some models have curves

Directions: Follow along with the slides and answer the questions in bold font in your journal.

Making models do yoga

  • In the previous lab, we saw that prediction models could be improved by including additional variables.'

    – But using straight lines for all the variables in a model might not really fit what's happening in the data.

  • In this lab, we'll learn how we can turn our lm() models using straight lines into lm() models using quadratic curves.

  • 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

  • Calculate the slope and intercept of a linear model that predicts audience_rating based on critics_rating for the training data.

    – Then create a scatterplot of the two variables using the testing data and use add_line() to include the line of best fit based on the training data..

    – Describe, in words, how the line fits the data? Are there any values for critics_rating that would make obviously poor predictions?

  • Compute the MSE of the model for the testing data and write it down for later.

Adding flexibility

  • You don't need to be a full-fledged 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 model it with a curve.

  • So instead of using an lm() like

    y = a + bx

  • We could use an lm() like

    y = a + bx + cx2

  • This is called a quadratic curve.

Making bend-y models

  • To fit a quadratic model in R, we can use the poly() function.

    – Fill in the blanks below to predict audience_rating using a quadratic polynomial for critics_rating.

    lm(____ ~ poly(____, 2), data = training)

  • What is the role of the number 2 in the poly() function?

  • Write down the model equation in the form:

    y = a + bx + cx2

  • Assign this model a name and calculate the MSE for the testing_data.

Comparing lines and curves

  • Create a scatterplot with audience_rating on the y-axis and critics_rating on the x-axis using your testing data.

    – Add the line of best fit for the training data to the plot.

    – Then use the name of the model in the code below to add your quadratic model:

    add_curve(____)

  • Compare how the line of best fit and the quadratic model fit the data. Use the difference in each model's testing MSE to describe why one model fits better than the other.

On your own

  • Create a model that predicts audience_rating using a 3 degree polynomial (called a cubic model) for the critics_rating using the training data.

    – By using a plot, describe why you think a 2 or 3 degree polynomial will make better predictions for the testing data.

    – Compute the MSE for the model with a 3 degree polynomial and use the MSE to justify whether the 2 or 3 degree polynomial fits the testing data better.

    – Using the linear model from above which has the smallest MSE, include a different numerical variable to the model and recompute the MSE. Does modeling the variable you chose as a quadratic polynomial improve the MSE further?