Learning objectives
The particular linear equation \[\hat{y} = b_0 + b_1x\] that satisfies the least squares criterion is called the least squares regression line. Casually, we often just call it the regression line,
Be sure to check the conditions for regression before reporting or interpreting a regression model.
Before starting, be sure to check the
- Quantitative Variable Condition: If either y or x is categorical, you can’t make a scatterplot and you can’t perform a regression. Stop.
From the scatterplot of y against x, check the
- Straight Enough Condition Is the relationship between y and x straight enough to proceed with a linear regression model?
- Outlier Condition Are there any outliers that might dramatically influence the fit of the least squares line?
- Does the Plot Thicken? Condition Does the spread of the data around the generally straight relationship seem to be consistent for all values of x?