Question

n = 5
ς(x - x̅)(y - ȳ) = 54
ς(y - ȳ)² = 112
ς(x - x̅)² = 30
r = 0.93
s_y = \sqrt{\frac{σ(y - ȳ)²}{n - 1}}
s_x = \sqrt{\frac{σ(x - x̅)²}{n - 1}}
b = r\frac{s_y}{s_x}
use the values and formulas above to calculate the slope.
1.56
1.79
1.61
1.04
0.91

Explanation:

Step1: Calculate $s_y$

Given $n = 5$ and $\sum(y-\bar{y})^2=112$, then $s_y=\sqrt{\frac{\sum(y - \bar{y})^2}{n - 1}}=\sqrt{\frac{112}{5-1}}=\sqrt{\frac{112}{4}}=\sqrt{28}=2\sqrt{7}\approx5.29$

Step2: Calculate $s_x$

Given $n = 5$ and $\sum(x-\bar{x})^2 = 30$, then $s_x=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}=\sqrt{\frac{30}{5 - 1}}=\sqrt{\frac{30}{4}}=\sqrt{7.5}\approx2.74$

Step3: Calculate the slope $b$

Given $r = 0.93$, $s_y\approx5.29$, $s_x\approx2.74$, then $b=r\frac{s_y}{s_x}=0.93\times\frac{5.29}{2.74}\approx0.93\times1.93 = 1.79$

Answer:

1.79