Load libraries

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

Let’s have a quick look at the data:

✔ Reading from "2025Scrabble (Responses)".

✔ Range 'Form Responses 1'.

head(scrabble)

# A tibble: 6 × 2
  Letters Score
    <dbl> <dbl>
1      11    27
2       7    12
3       5    12
4       7    24
5       6     8
6       8    17

Let’s visualize the data with a scatterplot, overlaying the reggression 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)


Call:
lm(formula = Score ~ Letters, data = scrabble)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.7395 -3.7950 -0.4614  1.8722 10.2605 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.2925     2.0678   0.625    0.537    
Letters       1.7782     0.2674   6.649 2.31e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.653 on 30 degrees of freedom
Multiple R-squared:  0.5957,    Adjusted R-squared:  0.5822 
F-statistic: 44.21 on 1 and 30 DF,  p-value: 2.311e-07

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")

       fit      lwr      upr
1 19.07402 16.76276 21.38528

scrab.pred(Letters=10, interval="prediction")

       fit      lwr      upr
1 19.07402 9.293873 28.85416

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.