An Investigation into Regression Model using EVIEWS

Prepared by: Sayed Hossain Lecturer for Economics Multimedia University Personal website: www.sayedhossain.com Email: sayed.hossain@yahoo.com

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Seven assumptions about a good regression model 1. 2. 3. Regression line must be fitted to data strongly. Most of the independent variables should be individually significant to explain dependent variable Independent variables should be jointly significant to influence or explain dependent variable. The sign of the coefficients should follow economic theory or expectation or experiences or intuition. No serial or auto-correlation in the residual (u) The variance of the residual (u) should be constant meaning that homoscedasticity The residual (u) should be normally distributed.2

4.5. 6. 7.

(Assumption no. 1)Regression line must be fitted to data strongly (Goodness of Data Fit)

*** Guideline : R2 => 60 percent (0.60) is better

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Goodness of Data Fit Data must be fitted reasonable well. That is value of R2 should be reasonable high, more than 60 percent. Higher the R2 better the fitted data.

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(Assumption no. 2) Most of the independent variables should be individually individually significant ** t- testt test is done to know whether each and every independent variable (X1, X2 and X3 etc here) is individually significant or not to influence the dependent variable, that is Y here.5

Individual significance of the variable Most of the independent variables should be individually significant. This matter can be checked using t test. If the p-value of t statistics is less than 5 percent (0.05) we can reject the null and accept alternative hypothesis. If we can reject the null hypothesis, it means that particular independent variable is significant to influence dependent variable in the population.6

For Example>>Variables:We have four variables, Y, X1, X2 X3 Here Y is dependent and X1, X2 X3 are independent Population regression model Y = Bo + B1X1+ B2X2 + B3X3 + u Sample regression model Y = bo + b1X1+ b2X2 + b3X3 + e Here, sample regression line is a estimator of population regression line. Our target is to estimate population regression line (which is almost impposible or time and money consuming to estimate) from sample regression line. For example, small b1, b2 and b3 are estimators of big B1, B2 and B3

Here, u is the residual for population regression line while e is the residual for sample regression line. e is the estimator of u. We want to know the nature of u from e.

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TipsIf the sample collection is done as per the statistical guideline (several random procedures) then sample regression line can be a representative of population regression line. Our target is to estimate the population regression line from a sample regression line.

Setting hypothesis for t test : An exampleNull Hypothesis: Bo=0 Alternative hypothesis: Bo0 Null hypothesis : B1=0 Alternative hypothesis: B10 Null Hypothesis : B2=0 Alternative hypothesis: B20 Null Hypothesis : B3=0 Alternative hypothesis: B3 0 Hypothesis setting is always done for population, not for sample. That is why we have taken all big B (from population regression line) but not small b from sample regression line.9

Hypothesis SettingNull hypothesis : B1=0 Alternative hypothesis: B10

Since the direction of alternative hypothesisis is , meaning that we assume that there exists a relationship between independent variable (X1 should be here) with dependent variable (Y here) in the population. But it can not say whether the relationship is negative or positive. This direction is a two tail hypothesis.

Null hypothesis : B1=0 Alternative hypothesis: B1