Evaluating and Improving Predictions

STAT 20: Introduction to Probability and Statistics

Agenda

• Announcements
• Reading Questions
• Break
• Worksheet

Announcements

• Portfolio (four worksheets) due Friday at 5pm.

• Quiz 4 is next Thursday. Two sided, handwritten cheatsheet is allowed.

Reading Questions

• Please put your laptops under your desk and your phones away.
• Write your name, ID, and bubble in Version “A” on your answer sheet.
• You may work only with those at your table!

Compare \(r\) and \(R^2\), selecting all of the statements which are true.

• A: \(r\) is a summary statistic between numerical variables that is often computed before a linear model is fit; \(R^2\) is fit to assess the performance of the linear model once it is fit.

• B: Both \(r\) and \(R^2\) can take values between 0 and 1.

• C: When fitting a linear regression model which involves multiple predictor variables, the goal is to fit a model which maximizes \(r\).

00:40

When adding a new variable to a linear regression model, what will happen to the \(R^2\) value as compared to what it was before?

• A: The \(R^2\) value will either be equal to what is was before, or less.
• B: We cannot determine this information.
• C: The \(R^2\) value will either be equal to what it was before, or greater.

00:30

When applying a transformation to a predictor variable before fitting a linear model (for example, squaring the predictor variable), the resulting function that describes the model is a _____ function of the transformed variable and a ____ function of the original variable.

• A: non-linear; non-linear
• B: linear; non-linear
• C: linear; linear
• D: non-linear; linear

00:40

You would like to generate predictions for new_x with a linear model that you built called m1. What data type/data structure does the argument supplied to newdata, new_x, need to be?

predict(object = m1, newdata = new_x)

• A: vector
• B: logical
• C: integer
• D: data frame
• E: factor

00:30

Break

05:00

Worksheet: Evaluating and Improving Predictions

30:00

Appendix - More practice!

Concept Questions

Which two models will exhibit the highest \(R^2\)?

01:00

This is a repeat of a previous CQ, but now with a linear model and a different characteristic of interest: R^2. The two highest R^2 values should be clearly B and E. The second two are very difficult to discern based on these plots.

This is a good time to mention that for a least squares linear models, R^2 is indeed just the square of the Pearson correlation coefficient. This isn’t true of non-linear models.

# A tibble: 4 × 5
  name    hours cuteness food_eaten is_indoor_cat
  <chr>   <dbl>    <dbl>      <dbl> <lgl>        
1 castiel    12      9          175 TRUE         
2 frank      18     10          200 TRUE         
3 luna       19      9.5        215 FALSE        
4 luca       10      8          218 FALSE        

m1 <- lm(formula = hours ~ cuteness + food_eaten + is_indoor_cat, 
         data = cats)

      (Intercept)          cuteness        food_eaten is_indoor_catTRUE 
    -3.800000e+01      6.000000e+00      2.815002e-16     -4.000000e+00 

How many hours does the model predict Frank will sleep each day? Write out the linear equation of the model from the model output to help you.

03:00

Which is the most appropriate non-linear transformation to apply to time_being_pet?

01:00

Worksheet

25:00

Lab

45:00