Linear Regression

Question 1

When to use linear Regression?

Answer 1

If knowing the correlation isn´t enough. We want to find out more about the relation.

Question 2

How to calculate linear regression using least square method?

Answer 2

1. Calculate mean of x and y. This is the point where the linear regression line has to get through. p.e. (3/4)
2. Take the simple linear regression equation
   ŷ = b0 + b1*x to calculate the slope (b1). The formula is Sum(x-xmean)(y-ymean) / Sum(x-xmean)**2
3. calculate the y-intercept by taking the x/y mean point from the beginning, in this case (3/4), and put it in the regression equation to easily find b0.
4. State the final regression equation for that case by fillin in slope and intercept. p.e. ŷ=1.6+0.7x

Question 3

What is the simple linear regression equation?

Answer 3

ŷ = b0 + b1*x

ŷ=the predicted value of y (the dependent variable) in a regression equation.
b1=slope
b0= y-intercept

Question 4

What does R-squared tell us?

Answer 4

How well a regression line actually predicts the values 1.0 would be the perfect prediction.

Question 5

How to calculate R-squared?

Answer 5

1. Take the linear regression equation (with intercept and slope calculated) at hand. P.e. it could be ŷ=1.6+0.7x
2. Put in the x values of your points in the equation and calculate ŷ.
3. Now put everythin in the formula of R-squared

Sum(ŷ-ymean)2
______________
Sum (y-ymean)2