Practice Residuals in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A residual is the difference between an observed data value and the value predicted by a statistical model, calculated as \text{residual} = y_{\text{observed}} - y_{\text{predicted}}. Positive residuals mean the model underestimated; negative residuals mean it overestimated.
If your model predicts 80 but the actual value is 85, the residual is +5. Residuals are 'leftovers' - what the model couldn't explain. Patterns in residuals reveal model problems.
Example 1
hardA regression model predicts \hat{y} = 30 for a data point, but the actual value is y = 35. Calculate the residual and interpret it.
Example 2
hardA residual plot shows a clear U-shaped pattern. What does this indicate about the regression model?
Example 3
hardGiven \hat{y} = 20 + 4x and actual data points (2, 30), (3, 33), (4, 35), find the residual for each point.
Example 4
hardA model predicts values 18, 22, and 26 for three points, while the actual values are 20, 21, and 30. Find the residuals and identify which point has the largest underprediction.