An extension of bivariate regression where researchers examine the effects of two or more independent variables on the dependent variable.

See explanation below.

Step-by-step explanation:

If we assume a linear model with two variables and one intercept the model is given by:

The extension of this to a multiple regression modelwith p predictors is:

We assume that we have n individuals

And the distribution for the errors is

and we can write this model with a design matrix X like this:

a nx1 response vector

represent the design matrix nx(p+1)

Where is a nx1 vector of ones, and is a (p+1)x1 vector of coeffcients

And is a nx1 error vector

Using ordinary least squares we need to minimize the following quantity:

And for this case if we find the best estimator for we got:

And the fitted values can be written as:

Where

In order to see if any coefficnet is significant we can conduct the following hyppthesis:

Null hypothesis:

Alternative hypothesis:

For some j in {0,1,....,p}

We need to use the following statistic:

Where

And are square roots of the diagonals of the diagomals of

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4