Line of Best Fit Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardTwo students draw different lines of best fit through the same scatter plot. Student A's line: (sum of squared residuals = 40). Student B's line: (sum of squared residuals = 28). Which line is better and why?
Solution
- 1 Step 1: The best line of fit minimises the sum of squared residuals (SSR). Student A: SSR = 40. Student B: SSR = 28.
- 2 Step 2: Student B's line is better because it has a smaller sum of squared residuals, meaning the data points are collectively closer to line B than to line A.
Answer
Student B's line () is better because its sum of squared residuals (28) is lower than Student A's (40), indicating a closer fit to the data.
The least-squares criterion defines the best line of fit as the one that minimises the sum of squared residuals. This objective measure allows us to compare different lines quantitatively. The least-squares regression line is the unique line that achieves the minimum possible SSR.
About Line of Best Fit
The line of best fit (trend line) is the straight line that best represents the overall trend in a scatter plot by minimizing the sum of squared vertical distances between the line and all data points. Its equation enables predictions for new x-values.
Learn more about Line of Best Fit →More Line of Best Fit Examples
Example 1 easy
A scatter plot shows the relationship between hours studied (x) and test score (y). The data points
Example 2 mediumGiven five data points: (1,3), (2,5), (3,6), (4,8), (5,11). Estimate the line of best fit by finding
Example 3 mediumA line of best fit for temperature (°C, [formula]) vs ice-cream sales (units, [formula]) is [formula