Activity: Simple Linear Regression

Height vs. Shoe Size

Objective

You will:

  • Identify predictor (height) and response (shoe size).
  • Explain what the slope means in context.
  • Recognize variability and limitations of small-sample regressions.
  • Experience how combining data strengthens inference.

Instructions

  1. Form a group of 4 or 5. (This is your sample size!)

  2. Collect your data. Each person will share their height and shoe size!

    • Height (\(X\)): inches (Use feet-to-inch conversion to help you get your height in inches.)
    • Shoe Size (\(Y\)): US

  3. Make a R data frame. (Replace my numbers with your data!)

df <- data.frame(height = c(69, 74, 77, 60, 62), 
                 size = c(11, 10.5, 12, 9.5, 9))
df
  height size
1     69 11.0
2     74 10.5
3     77 12.0
4     60  9.5
5     62  9.0
  1. Analyze within your group.
# (a) Plot your data. Height on the x-axis, Shoe Size on the y-axis.
plot(x = ______, y = _______)
# (b) Fit the simple linear regression model
model <- lm(____ ~ ____)

# (c) Draw the fitted regression line.
abline(______)
# (d) Obtain the estimated slope. What does it mean in context? Is the effect statistically significant?

Discussion

  • How does your group’s pattern compare to the overall line?
  • What does the slope mean in context?
  • Why might individual data vary around the line?
  • Would it make sense to predict shoe size for someone far outside our data range (e.g., 7’3” tall)? Why or why not?