Least Squares Regression Line Math Example 1

Solution

1. 1
   $\bar{x} = 3$, $\bar{y} = 4$; $s_x = \sqrt{2.5} \approx 1.58$; $s_y = \sqrt{1.5} \approx 1.22$
2. 2
   Calculate $r$: $\sum(x_i-\bar{x})(y_i-\bar{y}) = (-2)(-2)+(-1)(0)+(0)(1)+(1)(0)+(2)(1) = 4+0+0+0+2=6$; $r = \frac{6}{4 \times s_x \times s_y} = \frac{6}{4(1.58)(1.22)} = \frac{6}{7.71} \approx 0.778$
3. 3
   Slope: $b = r \frac{s_y}{s_x} = 0.778 \times \frac{1.22}{1.58} \approx 0.778 \times 0.772 \approx 0.60$
4. 4
   Intercept: $a = \bar{y} - b\bar{x} = 4 - 0.60(3) = 4 - 1.8 = 2.2$