Regression analysis using SPSS

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Regression Analysis

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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

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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

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Data Types:
Variables in the regression analysis must be metric.
Variables used for regression analysis are
•Price
•Cost
•Demand
•Supply
•Income
•Taste and Preferences

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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:

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• Linearity:
-Straight line relationship between two variables is termed as linear
relation or linearity.

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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.

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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.

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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.

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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.

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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.

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Thank
you 