Evaluating and Improving Predictions

STAT 20: Introduction to Probability and Statistics

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