First, let's parse through the information that's given us in the problem.

We're told that the standard deviation of percentage living in poverty is 3.1%.

So we can say that s,y is 3.1%.

Because remember, poverty is our response variable.

And we are also told that the standard deviation of percentage

of high school graduates is 3.73% so that x is 3.73%.

We are also given the correlation co-efficient as negative

0.75 so putting all of these in the formula For the slop.

B1 equals Sy over Sx times R.

We simply need to plug in the numbers, 3.1 divided by 3.73 times

negative 0.75, gives us a slope of negative 0.62.

Note that the sine of the slope is always going

to be equal to the sine of your correlation coefficient.

Conceptually speaking, this is true, because

we're clearly seeing a negative relationship

between the two variables so it makes sense that the slope is negative.

Mathematically speaking, remember that the standard deviation

is the square root of the variants.

And it's a measure of variability.

So the standard deviation of y and x are

always going to necessarily have to be positive numbers.

In the first part of the equation, we're dividing two

positive numbers, which is always going to yield a positive response.

And then we're multiplying by a value that could be negative or

positive, depending on, on the direction

of the relationship between the two variables.

So mathematically speaking as well, the sign of the slope is always

going to be the same as the sign of the correlation coefficient.