AP Statistics / Unit 5: Regression Analysis
5.5 Least-Squares Regression
Notes
The least-squares regression line minimizes the sum of squared residuals.
- $\displaystyle b=r\frac{s_y}{s_x}$, and it passes through $(\bar x,\bar y)$.
- $r^2$: the proportion of variation in $y$ explained by the linear model with $x$.
- $s$: typical size of a residual.
- Points with high leverage (extreme $x$) can be influential.
Practice
$r=0.8$, $s_y=10$, $s_x=2$. The slope $b=$
$\displaystyle 0.8\cdot\frac{10}{2}$.
$r^2=0.64$ means:
Explained variation.
The LSRL always passes through:
A property of least squares.
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