Question

question number 7. suppose that you are given the following results. find the correlation coefficient of the data. s_x = 16.026, s_y = 13.300, b = -0.810 o 0.976 o -0.976 o 0.025 o -0.025 o -0.488 o none of the above

Explanation:

Step1: Recall correlation - slope formula

The formula for the slope $b$ of the regression line in terms of the correlation coefficient $r$, the standard - deviation of $x$ ($s_x$) and the standard - deviation of $y$ ($s_y$) is $b = r\frac{s_y}{s_x}$. We need to solve for $r$.

Step2: Rearrange the formula for $r$

Rearranging the formula $b = r\frac{s_y}{s_x}$ gives $r=b\frac{s_x}{s_y}$.

Step3: Substitute the given values

We are given that $s_x = 16.026$, $s_y = 13.300$, and $b=-0.810$. Substitute these values into the formula for $r$:
\[
r=-0.810\times\frac{16.026}{13.300}
\]
\[
r=-0.810\times1.205
\]
\[
r=- 0.976
\]

Answer:

-0.976