Load libraries

library(mosaic)
library(dplyr)
library(googledrive)
library(googlesheets4)

Let’s have a quick look at the data:

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ℹ The googlesheets4 package is using a cached token for 'jfieberg@umn.edu'.
✔ Reading from "2026Scrabble (Responses)".
✔ Range 'Form Responses 1'.
head(scrabble)
# A tibble: 0 × 2
# ℹ 2 variables: Letters <lgl>, Score <lgl>

Let’s visualize the data with a scatterplot, overlaying the regression line:

gf_point(Score~Letters, data=scrabble) %>% gf_lm()

And, now fit the linear regression model:

lm.scrab<-lm(Score~Letters, data=scrabble)
summary(lm.scrab)

Exercises

  • Review interpretation of intercept and slope
  • Calculate Y^ for your name
  • Calculate a CI for the slope using the summary output
  • Know how to calculate the info in the 3rd and 4th columns of the summary output
  • Know how to interpret R^2 and residual standard error (i.e., sigma^) Predictions and confidence intervals
scrab.pred<-makeFun(lm.scrab)
scrab.pred(Letters=10, interval="confidence")
scrab.pred(Letters=10, interval="prediction")

How do we interpret these intervals?

  • confidence interval: I am 95% sure that the mean scrabble score among individuals that have 10 letters in their name is between 17.47 and 20.16.
  • prediction interval: I am 95% sure that the scrabble score for an individual with 10 letters in their name is between 17.47 and 20.16.