Question

question 1 of 10
to find the equation of a regression line, $hat{y}=ax + b$, you need these formulas:
$a = r\frac{s_y}{s_x}$ $b=\bar{y}-a\bar{x}$
a data set has an $r$-value of 0.885. if the standard deviation of the $x$-coordinates is 5.768, and the standard deviation of the $y$-coordinates is 8.112, what is the slope of the line to three decimal places?

Explanation:

Step1: Identify the formula for slope

The formula for the slope $a$ of the regression - line is $a = r\frac{s_y}{s_x}$, where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the $y$ - coordinates, and $s_x$ is the standard deviation of the $x$ - coordinates.

Step2: Substitute the given values

We are given that $r = 0.885$, $s_y=8.112$, and $s_x = 5.768$.
Substitute these values into the formula: $a=0.885\times\frac{8.112}{5.768}$.
First, calculate $\frac{8.112}{5.768}\approx1.4064$.
Then, $a = 0.885\times1.4064\approx1.245$.

Answer:

$1.245$