1. Simple Linear Regression
Using one variable to …
1) explain the variability of another variable
2) predict the value of another variable
Both accomplished with the line that best fits a scatterplot.
Linear Regression

2. Coefficient of Determination
Proportion of the total variability in the response variable explained away by knowing the value of the explanatory variable
Abbreviated with r2
Linear Regression

3. Variability Explained Variability Explained
Visualizing r2
r2 =
Variability Explained
Total Variability in y
Variability Explained
Height
Weight
Total Variability
in Y
Vrbility
Remain
Linear Regression

4. r2 doesn’t depend on x because of homoscedasticity
Variability Explained
Height
Weight
Total Variability
in Y
Vrbility
Remain
Linear Regression

5. Coefficient of Determination
Proportion of the total variability in the response variable explained away by knowing the value of the explanatory variable
Abbreviated with r2
0 < r2 < 1
Closer to 1 is a stronger relationship
Closer to 1 gives better predictions
Linear Regression