This document discusses multiple regression analysis. It defines multiple regression as a method for modeling a dependent variable as a function of several independent variables. There are three main methods for entering predictor variables: simultaneous entry, stepwise entry, and hierarchical entry. Simultaneous entry treats all predictors equally, stepwise entry adds predictors based on statistical criteria, and hierarchical entry adds predictors in predetermined stages. The document also outlines some key outputs of multiple regression analysis including R, R-squared, adjusted R-squared, regression coefficients, beta coefficients, t-statistics, and F-values. It explains what each of these values represents.

1. ANAGHA SINGH
Student Id:-
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AFFILIATION :- BANARAS HINDU
UNIVERSITY

2.  Method for studying the relationship between a
single criterion value(D.V.) and several predictor
values(I.V.).
 A dependent variable is modeled as a function of
several independent variables with corresponding
coefficients, along with the constant term. Multiple
regression requires two or more predictor
variables, and this is why it is called multiple
regression.

3.  Simultaneous: all predictor variables are entered
together.
 Stepwise/Statistical: predictor variables are
entered according to some order.
• By size or correlation with criterion variable
• In order of significance
 Hierarchical: predictor variables are entered in
stages.

4.  It is a standard method also known as ‘enter-
method’ of multiple regression analysis in
SPSS.
 In this model all predictor variables(IV) are
treated simultaneously on equal numbers .
Each predictor is assessed on criterion
variable.
 This method is most appropriate when we lack
a logical or theoretical basis for consideration.
 This is the safest method for calculating
multiple regression analysis.

5.  Also called ‘sequential method’.
 It is in many ways similar to the standard multiple
regression method, the only difference is being in the
way predictors are entered in the model.
 The researcher enter predictors into the model in a
particular order/sequence, determined by theoretical
background or on the basis of previous researches.
 If you have no reason to believe that one variable is
likely to be more important than anothuer variable,
than this model should not be used.

6.  The following steps are followed for the multiple
regression analysis:-
• R
• R²
• Adjusted R²
• R² change
• B
• ß
• T
• F value

7.  R- value of multiple correlation between variables.
It has no +ve/-ve signs. It reflects the degree of
association.
 R²- it’s a correlation coefficient square. It indicates
the percentage of total variance.
 Adjusted R²- it gives a sum idea that how well
relationship can be justified. It is calculated only for
those variables whose addition is in the model.

8.  R² change- modified value of ‘adjusted R²’. In
modern statistics this is the adequate value of
percentage which proves the regression model.
 B- the un-standardized value of regression
coefficient which indicates the rate of change per
unit. ‘B’ is the slope of line in linear regression.
 ß- the standardized regression coefficient which is
an important part in regression model. It tells the
direction(+ve/-ve) of the coefficient. Higher beta
value indicates greater impact of predictor.