Statistics

The residuals for data set A and data set B were calculated for a linear model and plotted on separate residual plots. The residuals for data set A form a pattern. The residuals for data set B do not form a pattern. A linear model would be a good fit for which data set(s)?

Step-by-step solution with explanation

Final Answer

Data set B. Because its residuals show no pattern (random scatter), the linear model is a good fit. Data set A's residuals form a pattern, which means a linear model is NOT a good fit for it.

Step-by-step solution

1

Understand what a residual plot shows

A residual is the difference between the real data point and what the linear model predicted. We plot these differences to see if a linear model fits the data well.
2

Interpret a residual plot with a pattern

If the residuals form a pattern (like a curve or wave), it means the linear model is missing something. The data has a non-linear relationship that the straight line cannot capture.
3

Interpret a residual plot with no pattern

When residuals are scattered randomly with no pattern, the linear model explains the data well. The errors are just random noise, not a hidden curve or trend.
4

Apply the rule to data set A

Since the residuals for data set A form a pattern, the linear model does not fit it well. A different model (like a quadratic) might work better.
5

Apply the rule to data set B

Since the residuals for data set B are randomly scattered with no pattern, the linear model is a good fit for this data set.

Understanding this problem

Learning Insight

A residual plot is like a 'leftover clue' detector. If the leftovers (residuals) still have a shape or pattern, your model missed that shape. A truly good model leaves only random noise behind — no hidden structure in the residuals.

Quick Tip

Pattern in residual plot = BAD fit. Random scatter = GOOD fit. Just remember: 'Pattern is a Problem.'

Common Mistake

Students often think a residual plot with points both above and below zero is bad. That is actually what you WANT — random scatter above and below zero means the model is fitting well, not poorly.