Home › AP Statistics › Statistics › Linear Regression and Correlation › Interpreting the slope b in a fitted line means …
Interpreting the slope b in a fitted line means reading it as the change in y for:
AA one-unit rise in y
BA doubling of x
CA halving of x
DA one-unit rise in x
Answer & Solution
Correct answer: D. A one-unit rise in x
1. The slope is the ratio of vertical change to horizontal change.
2. For the linear equation y = a + bx, b is the slope and a is the y-intercept.
3. Increasing x by one therefore increases the predicted y by b.
4. That is what makes the slope the quantity of practical interest in a regression.
5. Doubling or halving x would change y by an amount depending on where you started.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 12 'Linear Regression and Correlation', sections 12.1-12.6_
Related questions
An outlier in a regression analysis shows up in a residuals plot as a point that is:Least-squares regression earns its name because the fitting rule minimises the sum of the The error term for a single data point is written as the observed y minus the:The scatter plot and the residuals plot are read differently: the scatter plot should lookA scatter plot of data suited to linear regression should resemble:Alongside the line itself, the other quantity calculated and interpreted in this analysis A pattern left in a residuals plot suggests that:A residuals plot done correctly should appear: