Question

Calculate a linear regression, the residuals, and the correlation between two variables using the following info: number of people:12,14,15,18,20,16,14,13,18,19,20,22 and
cost of drinks:24,30,36,38,65,44,36,30,39,76,80,85

Answer 1

Using an online calculator, I have the following:

12 data pairs (x,y):
( 12.0 , 24.0 ); ( 14.0 , 30.0 ); ( 15.0 , 36.0 ); ( 18.0 , 38.0 ); ( 20.0 , 65.0 ); ( 16.0 , 44.0 ); ( 14.0 , 36.0 ); ( 13.0 , 30.0 ); ( 18.0 , 39.0 ); ( 19.0 , 76.0 ); ( 20.0 , 80.0 ); ( 22.0 , 85.0 );

Regression equation:
predicted y = -53 + 6.06x

Correlation: r = 0.894

To find residuals:
Y(hat) comes from substituting an x value into a regression equation and solving for y(hat). Y(hat) is also called the predicted y value in a regression equation.

Let's use an example. Suppose the regression equation is this:
y(hat) = 2.75 + .5x

If x = 1, then y(hat) = 3.25

Suppose y = 3. Then y - y(hat) would be 3 - 3.25 = -0.25 (using the above example). This would be your residual.

The residuals in regression are measuring how far each observed y is from the regression line, y(hat), for a given value of x.

I hope this helps.