Line of Best Fit Statistics Example 1
Follow the full solution, then compare it with the other examples linked below.
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 . (a) Interpret the slope. (b) Predict the score for a student who studies 8 hours.
Solution
- 1 Step 1: (a) The slope is 5, meaning for each additional hour studied, the predicted test score increases by 5 points.
- 2 Step 2: (b) Substitute : .
- 3 Step 3: The predicted score is 80. This is an interpolation if 8 hours is within the range of the data, or an extrapolation if it is outside the data range.
Answer
(a) Each additional hour of study is associated with a 5-point increase in test score. (b) Predicted score for 8 hours: 80.
The line of best fit summarises the linear relationship between two variables. The slope represents the rate of change, and the y-intercept is the predicted value when . Predictions are most reliable within the range of observed data (interpolation) and less reliable outside it (extrapolation).
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 2 medium
Given 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
Example 4 hardTwo students draw different lines of best fit through the same scatter plot. Student A's line: [form