RESEARCH METHOD COHEN ok

REGRESSION ANALYSIS 541
Box 24.35
Significance level in multiple regression analysis
ANOVA b
Model Sum of squares df Mean square F Sig.
1 Regression 7969.607 3 2656.536 643.116 0.000 a
Residual 190.013 46 4.131
Total 8159.620 49
Chapter 24
a. Predictors: (Constant), Level of interest in the subject, Intelligence, Hours of study
b. Dependent variable: Level of achievement
Box 24.36
The beta coefficients in a multiple regression analysis
Coefficients a
Unstandardized coefficients
Standardized coefficients
Model B SE Beta t Sig.
1 (Constant) 21.304 10.675 1.996 0.052
Hours of study 9.637 1.863 0.920 5.173 0.000
Intelligence −6.20E-02 0.133 −0.062 −0.466 0.644
Level of interest in the
subject
0.116 0.135 0.131 0.858 0.395
a. Dependent variable: Level of achievement
The only independent variable that has a
statistically significant effect on the level of
achievement is ‘hours of study’.
So, for example, with this knowledge, if we knew
the hours of study, the IQ and the level of
measured interest of a student, we could predict
his or her expected level of achievement in the
examination.
Multiple regression is useful in that it can
take in a range of variables and enable us to
calculate their relative weightings on a dependent
variable. However, one has to be cautious:
variables may interact with each other and may be
intercorrelated (the issue of multicollinearity), for
example Gorard (2001) suggests that
poverty and ethnicity are likely to have some
correlation between themselves, so using both
together means that we end up using their common
variance twice. If collinearity is discovered (e.g. if
correlation coefficients between variables are higher
than .80) then one can either remove one of the
variables or create a new variable that combines the
previous two that were highly intercorrelated.
(Gorard 2001: 172)
Indeed SPSS will automatically remove variables
where there is strong covariance (collinearity). 2
In reporting multiple regression, in addition to
presenting tables (often of SPSS output), one can
use a form of words thus, for example:
Multiple regression was used, and the results include
the adjusted R square (0.975), ANOVA (ρ