Practice Line of Best Fit in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The straight line that best represents the trend in a scatter plot, minimizing the overall distance between the line and all data points.
If you stretched a rubber band through a scatter plot to be as close to all points as possible, that's the line of best fit. It captures the overall trend.
Example 1
easyA scatter plot shows the relationship between hours studied (x) and test score (y). The data points generally trend upward. A line of best fit has equation y = 5x + 40. (a) Interpret the slope. (b) Predict the score for a student who studies 8 hours.
Example 2
mediumGiven five data points: (1,3), (2,5), (3,6), (4,8), (5,11). Estimate the line of best fit by finding the slope using the first and last points, then adjust to pass through the centroid (\bar{x}, \bar{y}).
Example 3
mediumA line of best fit for temperature (°C, x) vs ice-cream sales (units, y) is y = 12x - 50. (a) Predict sales when it is 30°C. (b) Below what temperature does the model predict zero or negative sales? (c) Comment on the limitation.
Example 4
hardTwo students draw different lines of best fit through the same scatter plot. Student A's line: y = 3x + 2 (sum of squared residuals = 40). Student B's line: y = 2.5x + 4 (sum of squared residuals = 28). Which line is better and why?