Track 9 · Correlation and Regression · Lesson 4 of 15
Simple linear regression
Fit the least-squares line from data or summary statistics, use it to predict, and calculate residuals.
A juice brand's marketing team wants to know how many extra packs it sells, on average, for each additional thousand riyals of TV advertising in a week — and what sales to expect in a week with a planned 60 000 SAR campaign. A correlation says the two move together; a regression line says by how much.
Simple linear regression describes how a response changes, on average, with one explanatory variable , using a straight line . The hat on (“y-hat”) marks a fitted or predicted value. For each observation, the vertical gap between the actual and the fitted value is the residual:
A positive residual means the point lies above the line (the model under-predicts it); a negative residual means it lies below.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the least-squares slope and intercept from data or from r, the SDs and the means
- Use a fitted line to predict and calculate residuals (actual minus fitted)
- State the properties of the least-squares line
- Explain why a simple slope can absorb the effect of variables that move with x