Residuals Practice Worksheet

Residuals Practice Worksheet

Read each question carefully and answer to the best of your ability. Show all your work for calculation questions.

What is a Residual?

In statistics, a residual is the difference between the observed value (actual data point) and the predicted value (the value predicted by the regression line). It measures the vertical distance from the data point to the regression line.

Residual = Observed Value - Predicted Value

1. Which of the following best describes a residual?

2. A positive residual indicates that the observed value is:

3. If the observed value is 15 and the predicted value is 12, the residual is  .

4. A residual of zero means the data point lies directly on the  .

5. A researcher collects data on the number of hours studied (x) and the exam score (y) for 5 students. The regression line is given by ŷ = 5x + 50. Calculate the residuals for the following students:

a) Student A: Hours Studied = 3, Observed Score = 68

Predicted Score (ŷ) =  

Residual =  

b) Student B: Hours Studied = 5, Observed Score = 75

Predicted Score (ŷ) =  

Residual =  

c) Student C: Hours Studied = 2, Observed Score = 60

Predicted Score (ŷ) =  

Residual =  

6. For Student A in question 5, what does the sign of their residual tell you about their observed score compared to the predicted score?

7. Consider the scatter plot below with a regression line. Draw a vertical line from each data point to the regression line to visually represent the residuals.

This scatter plot shows data points and a dashed regression line.