Evaluating and Improving Predictions

STAT 20: Introduction to Probability and Statistics

Concept Questions

Which three 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 obtained by the models fit with B and E. The data in C has a positive enough trend that it should be identified as the third choice.

This is a good time to mention that for a least squares linear models, R^2 is indeed just the square of the 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. Hint: as an example, you can read 5e+01 as \(5* 10^1\).

03:00

Using “time being pet”, which lm formula is most appropriate to predict hunger, based on the below visualization?

01:00

Break

05:00

Problem Set: Evaluating and Improving Predictions

40:00

Lab

45:00