Introduction To Statistics

Lecture 32

Dr. MUMTAZ AHMEDMTH 161: Introduction To StatisticsReview of Previous LectureIn last lecture we discussed:

Simple Linear Regression ModelMethod of Ordinary Least Squares (OLS)Properties of OLSStandard Error of Regression (SER)Coefficient of Determination (R2)An Example

22Objectives of Current LectureIn the current lecture:

An example of Simple Linear Regression ModelIntroduction Multiple Linear Regression ModelAssumptions of Simple & Multiple Regression ModelsEstimation and Interpretation

33Regression: An Example4XY516619823102812361341154416451750Multiple Linear Regression ModelGeneral form of a Multiple Linear Regression Model:t=1,2,.,n

Where, yis are observations on dependent variable (y)xis (i=1,2,k) are k regressors each having n observations(i=1,2,,k) are regression coefficients or parametersuis are errors5

5Multiple Linear Regression ModelMultiple Linear Regression ModelAssumptions of Linear Regression ModelRegressor (X) and error term (u) are independent of each other, i.e. E(X, ui)=0Error are normally distributed with a mean of zero and a constant variance, i.e.

No Multicollinearity between regressor

Multiple Linear Regression ModelEstimating Least Squares Estimates via Normal EquationSimple linear regression model:Estimated regression model is:Normal Equation are:

Multiple Linear Regression ModelNormal Equation are:

Solving normal equations simultaneously, we get:

So estimated regression line is:

Multiple Linear Regression ModelEstimating Least Squares Estimates via Normal EquationMultiple linear regression model:Estimated regression model is:Normal Equation are:

Multiple Linear Regression ModelNormal Equation are:

Multiple Linear Regression ModelNormal Equation are:

Solving normal equations simultaneously, we get:

Multiple Linear Regression ModelExample:A statistician wants to predict the incomes of restaurants, using two independent variables, the number of restaurant employees and restaurant floor area. He collected the following data:Calculate:Estimated linear regression equation.

Solution:Do the demo in Excel13YX1X2301015225816101273714210ReviewLets review the main concepts:

An example of Simple Linear Regression ModelIntroduction Multiple Linear Regression ModelAssumptions of Simple & Multiple Regression ModelsEstimation and Interpretation

14Final WordBest of Luck in the course15