A scatterplot shows one point per individual, using two measurements as coordinates.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The line of fit
A line of best fit runs through the middle of the cloud, as close to as many points as possible.
Interpreting slope
The slope is the predicted change in y for a one-unit rise in x. Naming its units turns it into a sentence.
Residuals
A residual is actual minus predicted. A positive residual means the model underestimated that point.
Residuals should look random
A clear curve in the residuals means a line was the wrong model, however good the fit appeared.
Still not causation
A good fit shows association. Only a controlled experiment can establish cause.
Direction, form, strength
A complete description of a scatterplot names all three, plus any unusual points. Positive or negative, linear or curved, and how tightly the points follow the pattern.
A line of fit is a linear model
The slope predicts the change in the response per unit change in the explanatory variable, in context and with units. That interpretation is what turns a fitted line into information.
Residuals check the fit
Residual is observed minus predicted. A random scatter of residuals supports a linear model; a curved pattern means the line is the wrong shape, however close the points look.
Do not predict far outside the data
A fitted line describes the range observed. Extending it well beyond assumes the relationship continues, which the data do not support and which produces confident nonsense.
Step 2: Try It Yourself
Tap and try it out.
The slope is 1: for every 1 across, the line goes 1 up.
Step 3: Watch an Example
One step at a time.
Watch Diego Compute a Residual
A model predicts y = 2x + 1. At x = 4 the actual value was 11.
- Step 1
The prediction at x = 4 is 2(4) + 1 = 9.
Step 4: Your Turn
Practice makes it stick.
The Residual
Problem 1 of 2
Predicted 9, actual 11. What is the residual?
The Prediction
Problem 2 of 2
y = 2x + 1 at x = 6. What is the predicted value?
Fit and Check
1 of 8
y = 3x + 2 at x = 5. Predicted value?
2 of 8
Predicted 17, actual 14. Residual?
3 of 8
A negative residual means the model did what? 1 overestimated, 2 underestimated.
4 of 8
A model has slope 4 dollars per hour. Predicted rise for 3 more hours, in dollars?
5 of 8
y = 0.5x + 10 at x = 20. Predicted value?
6 of 8
Does a good line of fit prove causation? 1 yes, 0 no.
7 of 8
Put the fitting process in order.
- 1Check whether the pattern looks linear.
- 2Fit a line through the middle of the cloud.
- 3Check the residuals for a leftover pattern.
- 4Plot the data as a scatterplot.
8 of 8
Predicted 25, actual 25. Residual?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Predicted 30, actual 34. What is the residual?
Question 2 of 2
What should a residual plot look like for a good linear model?
What You Learned
- A line of fit runs through the middle of a scatterplot.
- Its slope predicts the change in y per unit of x.
- Residuals are actual minus predicted, and should scatter randomly.