Chapter 8 - Linear Regression
| Thursday, 22 September 2022 | |
| 1-minute read | |
| 173 words | |
Line of Best Fit
\[ \hat{y} = a + bx \]
Points on the line of best fit are predicted y-values, which is why $\hat{y}$ notation is used.
The value of $r^2$ is the percent of the data's variation in the y-value that is accounted for by the variation of the x-value.
Example
Explanatory variable: miles traveled in a car
Response variable: gallons of gasoline used
R-squared value: 0.87
This means 87% of the change of gallons can be attributed to the change in miles traveled in a car.
Residuals
Residuals show how much individual data points differ from their corresponding predicted values.
Their values can either be negative or positive.
\[ r = y - y_0 \]
If the residual plot is randomly scattered, then the data is linear. Otherwise, a pattern similar to higher degree functions may indicate a curve in the data.
92.2% of the change in calories can be attributed to its linear relationship with the change in the grams of fat. 8% can be attributed to unknown factors.