Statistical process, explanatory/response variables; Scatterplots; direction/form/strength of association; Pearson r and coefficient of determination; Outliers, causality and data validity; Linear regression, slope/intercept and residual plots; Exponential regression, interpolation/extrapolation and prediction reliability
Example 1
Fit the least-squares line y=mx+c to (0,2),(1,5),(2,5),(3,8). Find m. Round to 2 decimal places.
Show worked answer
Answer: 1.80
- Use m= Sxy divided by Sxx with deviations from the sample means.
- Rounded result: 1.80.
Example 2
For the data (0,3),(1,7),(2,8),(3,12), find the intercept of the least-squares line. Round to 2 decimal places.
Show worked answer
Answer: 3.30
- Compute the least-squares gradient, then c=mean(y)−m mean(x).
- Rounded result: 3.30.
Example 3
A regression model predicts y=5x+3. At x=1, observed y is 10. Find the residual.
Show worked answer
Answer: 2
- Residual = observed − predicted, so it equals 2.