Integrated Math 1 / Unit 7: Descriptive Statistics
7.5 Scatter Plots and Lines of Fit
Notes
A scatter plot shows two numerical variables as points $(x, y)$. A line of fit approximates the trend.
- Use two points on the line to find slope, then write $\hat{y} = mx + b$.
- Interpret slope as the predicted change in $y$ for each increase of 1 in $x$.
- A residual is actual $-$ predicted. Positive means the line underestimated.
- Interpolation (inside the data range) is more reliable than extrapolation (outside it).
Practice
A line of fit is $\hat{y} = 2.5x + 10$. What is the predicted $y$ when $x = 8$?
$2.5(8) + 10 = 20 + 10 = 30$.
The line $\hat{y} = 3.2x + 45$ predicts a test score from hours studied $x$. What does the slope 3.2 mean?
Slope is the predicted change in $y$ per 1 unit increase in $x$.
A student's actual score is 70 and the line of fit predicts 64. What is the residual?
Residual $=$ actual $-$ predicted $= 70 - 64 = 6$.
Ready for more? Take the Unit 7 test.