Analysis using SPSS - H.H.The Rajha's College
- 2. 2 Regression – Basic Concepts • What is regression analysis? - It is multivariate dependence technique used to find linear relationship between one metric dependent variable and more metric independent variables • When is regression analaysis used? - Identifies factors which contribute to take up that brand. - Identifies the factor which influences a consumer's impression on a brand - Identifies the features which make it more likely to buy that brand. • Regression model: - The two types of regression model are Simple regression Multiple regression
- 3. 3 Simple Regression: In Simple Regression only one dependent variable and only one independent variable is present in the analysis. Y = a + bX Where ‘a’ is intercept, ‘b’ is regression coefficient. Multiple Regression: In multiple Regression there are one dependent variable and more than one independent variables present in the analysis. Y = a + b1 X1 + b2 X2 +…+ bn Xn a is intercept, represents the amount of dependent Y when all independents are “0” & b’s are regression coefficients
- 4. 4 Data Types: Variables in the regression analysis must be metric. Variables used for regression analysis are •Price •Cost •Demand •Supply •Income •Taste and Preferences
- 5. 5 Normality: -The variables satisfying the properties of normal distribution is termed as normality. - This can be detected using pp-plot or qq-plot ie., plotting expected cumulative probability against observed cumulative probability is pp-plot. Terminologies:
- 6. 6 • Linearity: -Straight line relationship between two variables is termed as linear relation or linearity.
- 7. 7 Outliers: -Extreme values of a predictor or outcome variable that appear discrepant from the other values . Predicted values: -Also called fitted values, substituting the regression coefficient and the independent variables in the model we get the predicted values for each case. Residuals: -Residuals are the difference between the observed values and predicted values of the dependent variables.
- 8. 8 Beta weights: -Standardization of regression coefficient are called Beta Weights. Ratio of Beta weights are the ratio of relative predictive power of the independent variable. R-Square : -Proportion of the variation of dependent variable explained by the independent variable. Adjusted R-Square: -Proportion of the variation of dependent variable explained by the independent variable after adding or deletion of the variables. Multicollinearity: -Inter correlation among the independent variables.
- 9. 9 VIF (Variance Inflation factor): -It is a measure, used to find the amount of multicollinearity. -VIF= 1/tolerance=1/1-R2 -Higher the VIF indicates higher the multicollinearity. F Test: -F Test is used to test the R square and it is same as to testing the significance of the regression model. -Null hypothesis: The data doesn’t fit the model i.e., we have to reject the null hypothesis.
- 10. 10 Assumptions: • The variables should be metric variables. • The sample size should be adequate i.e., each variable should have at least ten observation. • Linearity among the dependent and independent should be satisfied. • Multicollinearity should be absent. • Residuals should be normally distributed. • Residuals should satisfy homoscedasticity property. • Residuals should be independent. • Multivariate normality for variables should be satisfied. • No outliers.
- 11. 11 Expected output: • Model should be significant i.e., (Pr>F) ≤ 0.05. • VIF should be ≤2. • Condition index should be ≤ 15. • Independent variable should be significant (Pr >t) ≤0.05. • Standard estimates tells us the amount of variance of dependent variable explained by that independent variable (tested using significance t test). • R square tells the amount of variance explained by the model on the whole (tested using significance F test). • Parameter estimates can be negative or positive.
- 12. 12 Thank you