SOLUTION: Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variab

Question 1196899: Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.25, and the standard deviation for y is 4.52. The regression equation is reported as
y=−3.5+1.77x

What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 0 and 1.)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The goal is to find the value, aka coefficient of determination

The regression line is of the form
y = a+bx
where,
a = y intercept = -3.5
b = slope = 1.77

There are a few formulas that we can use to calculate the slope b.
One of which is this

where,
r = correlation coefficient
Sy = sample standard deviation of the y values
Sx = sample standard deviation of the x values

Rearranging that formula to isolate r gets us

Then plug in these values
b = 1.77 = given slope
Sx = 1.25 = given standard deviation of the x values
Sy = 4.52 = given standard deviation of the y values

The calculation yields the following

Now square both sides

I'll let you round this however you want.
If you rounded to say four decimal places, then you'd get 0.2396; though be sure to follow the instructions your teacher provides.

So about 23.96% of the variation in y can be explained by the variation in x.

Note: keep in mind you won't enter a percentage as a final answer, but rather a decimal value between 0 and 1.

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