Question

n = 5
ς(x - x̄)(y - ȳ) = 31
ς(y - ȳ)² = 34
ς(x - x̄)² = 30
r = 0.97
s_y = √(σ(y - ȳ)²/(n - 1))
s_x = √(σ(x - x̄)²/(n - 1))
b = r(s_y/s_x)
use the values and formulas above to calculate the slope.
o 0.91
o 1.61
o 1.04
o 1.56
o 1.79

Explanation:

Step1: Calculate $s_y$

Given $\sum(y - \bar{y})^2=34$ and $n = 5$, then $s_y=\sqrt{\frac{\sum(y - \bar{y})^2}{n - 1}}=\sqrt{\frac{34}{5 - 1}}=\sqrt{\frac{34}{4}}=\sqrt{8.5}\approx2.915$

Step2: Calculate $s_x$

Given $\sum(x - \bar{x})^2=30$ and $n = 5$, then $s_x=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}=\sqrt{\frac{30}{5 - 1}}=\sqrt{\frac{30}{4}}=\sqrt{7.5}\approx2.739$

Step3: Calculate the slope $b$

Given $r = 0.97$, and using the formula $b=r\frac{s_y}{s_x}$, substitute the values of $r$, $s_y$ and $s_x$: $b = 0.97\times\frac{2.915}{2.739}\approx0.97\times1.064\approx1.04$

Answer:

1.04