In a linear regression model, we predict the dependent variable(y) with the help of independent variable.
Our aim is to minimize the residuals and make the best prediction.
Multicollinearity refers to the situation when there is correlation between the independent variables.
This could lead to wrong predictions and increase residuals
Multicollinearity can be checked with the help of VIF, variance inflation factor.
The industry accepted value of VIF is 5. A VIF greater than 5 means collinearity.
In order to treat multicollinearityy, we could plot scatter plot between different independent variables and remove one of the variable that is correlated.
Before running the linear regression model, we should make sure that there is no correlation between independent and dependent variable, residuals to be normally distributed, no auto correlation.
There are 8 numbers for the computer to choose from. So the probability of choosing a particular number is 1/8. The first number can be any one of the 8. The second and the third must be the same as the first, with probability 1/8.
Therefore the probability that all three numbers are the same = (1/8)(1/8) = 1/64 [ player will win a prize ] (=0.03125)