Line of Best Fit Statistics Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
mediumA line of best fit for temperature (°C, ) vs ice-cream sales (units, ) is . (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.
Solution
- 1 Step 1: (a) units. (b) Set : °C. Below 4.2°C the model predicts negative sales.
- 2 Step 2: (c) Negative sales are impossible — this shows the model's limitation outside the range of observed data. Linear models may not be valid for extrapolation beyond the data range.
Answer
(a) 310 units at 30°C. (b) Below about 4.2°C, the model predicts zero or negative sales. (c) The linear model breaks down outside the data range — extrapolation is unreliable.
Lines of best fit are useful for prediction within the data range but can give unrealistic results when extrapolated. Real-world relationships may not be linear across all values, so interpreting predictions from a linear model requires understanding its domain of validity.
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 4 hardTwo students draw different lines of best fit through the same scatter plot. Student A's line: [form