1. Residuals and Residual Plots

2. How close is the Line of Best Fit?
One additional method to determine if a linear model is appropriate for a data set is to analyze the residuals.
Do this by comparing the actual data point to the predicted outcome using the equation
A residual is the vertical distance between an observed data value and its predicted value using the regression equation.
A residual plot is a scatter plot of the independent variable on the x-axis and the residuals on the y-axis.
The Residual Value is the difference between the actual observed value and the value predicted by the equation
Residual value = observed value – predicted value

3. Use Residual Plots to Interpret Data
The shape of the residual plot can be useful to determine whether a linear model is a good fit for a data set or not
Linear:
If a residual plot results in no identifiable pattern or a flat pattern, then the data may be linearly related.
This means most of the data points were about the same distance from the line of best fit so the line had a strong correlation to the data

4. Use Residual Plots to Interpret Data
Non-Linear:
If there is a pattern in the residual plot, the data may not be linearly related. (it could have some type of non-linear relationship like quadratic, exponential, or none at all)

5. Residuals Example –Follow Along in Carnegie Book Lesson 3 pg 198-200
The table below shows data of the speed at which a car is travelling and the distance it takes to brake to a complete stop.

6. Residuals Example –Follow Along in Carnegie Book Lesson 3 pg 198-200
1. Construct a scatterplot and line of best fit)
2. Correlation coefficient
r = .99, strong positive linear association
3. The linear regression equation is
y = 5.4x - 134

7. Residuals Example pg199 Now calculate the residuals
First, use the linear regression equation to calculate the predicted braking distance (y value / output) for each speed (x value / input)
The linear regression equation is y = 5.4x - 134
Next, subtract:
Residual value = observed value – predicted value
The Residual Value is the difference between the actual observed value and the value predicted by the equation

8. Now Create a Residual Plot pg200
The residual plot is a scatter plot of the independent variable on the x- axis and the residuals on the y-axis.
It will show you how far away each actual data point is from the line of best fit
To Graph: keep the x axis the same (speed as the independent variable) and graph the residual value on the y axis