Multiple Regression

Question 1

What is, roughly speaking, the difference between linear and multiple regression?

Answer 1

Instead of having only one independent variable like in linear regression(thus, 2dim), you have several independent variables and therefore more dimensions. P.e. 4 dimensional, if you have 1 dependent and 3 independent variables

Question 2

What is multicollinearity?

Answer 2

if the independent variables do not only interact with the dependent variable but also under each other. We try to aviod that.
The aim is to find the IV who contribute to the DV but not interact which each other.

Question 3

Write down the formulas of Multiple Regression Model, Multiple Regression Equation, Estimated Multiple Regression Equation and tell the differences!

Answer 3

Multiple Regression Model: 
y = ß0 + ß1X1 + ß2X2 + ßpXp + E
# ß is beta and means variable
# ß0 is intercept
# x is the weight of the variable
#E is a round E and means error term

Multiple Regression Equation:
E(y) = ß0 + ß1X1 + ß2X2 + ßpXp
# E(y) is the expected value of y
# why no error term? Bc in the equation the error is assumed to be 0.

Estimated Multiple Regression Equation:
^y= b0 + b1X1 + b2X2 + bpXp
# ^y is the predicted value of y
# the b´s are the estimates of the ß´s

In practice you get/calculate a Multiple Regression Equation E(y) = ß0 + ß1X1 + ß2X2 + ßpXp with numbers:
E(y) = 12 + 3x1 + 6x2.
# 3 and 6 are the coefficients
# x1=capital inverstment
#x2=marketing expenditures
Now to test, you put in one variable and hold the other one constant. So if you put 100$ for capital investment(x1) you get an expected value of 312. If you put 100$ for marketing(x2), you get an expected value of 612 out of it.