Multiple regression - Case Study Example

Regression Analysis The following case study included framing a regression equation of Income on Age, education and working hours of the participants. Regression equation is the estimate of the relation between the dependant variable (criterion) with the independent variables (predictors). The independent variable chosen in our study was the Income while the independent variables were age, education and working hours of the participants. Hypothesis testing of the regression equation is based on the p value and the coefficient of determination R2.

The null hypothesis will contend that there is no significant relation of the dependant variable with the independent variables if the p value of the framed regression is more than the chosen level of significance which is considered as 0.05 levels. On the other hand the alternate hypothesis will contend that there is significant relation of the dependant variable with the independent variables if the p value of the framed regression is less than the chosen level of significance which is considered as 0.

05 levels (Lehman and Romano, 2005). Coefficient of determination is the association factor of the independent variables with the dependent one, more the value moves towards 100% the relation will be considered stronger and more it moves towards 0% the relations are considered weak Framed Regression Model for the case studyMultiple Linear Regression - Estimated Regression EquationIncome = +0.63123236633544 Age +1.6310151733801 Educ +0.6060166606298 HRS +0.

72543207253468 VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-valueAge[t]0.6312320.1860683.3924870.0007930.000397Educ[t]1.6310150.2027388.04492700HRS[t]0.6060170.1786073.3930180.0007920.000396Constant0.7254320.4674171.5520010.12180.0609VariablePartial CorrelationAge[t]0.199383Educ[t]0.434562HRS[t]0.199413Constant0.092682Critical Values (alpha = 5%)1-tail CV at 5%1.652-tail CV at 5%1.96Multiple Linear Regression - Regression StatisticsMultiple R0.501424R-squared0.251426Adjusted R-squared0.

243348Multiple Linear Regression - Analysis of VarianceANOVADFSum of SquaresMean SquareRegression39.0902313.030077Residual27827.0644050.097354Total28136.1546360.12866418487872F-TEST31.124327p-value0 From the above model it becomes evident as the p value is 0 which is