_assumptions of multiple regression analysis

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Assumptions of Multiple Regression Analysis

Following are the assumptions of multiple regression analysis:

Independence of observationIndependence of observation assumption implies that there should not exist any

relationship between the responses of any respondent with that of another respondent (Leech,

Barret & Morgan, 2005). Durbin-Watson test is used to test the check the presence of any serial

correlation among the residuals of the observations. Durbin-Watson test statistics for the

regression test of this study is 2.11. The values range from 0 to 4 however optimally it should be

between 1.5 and 2.5.

Normal Distribution of Data

The assumption of normal distribution of data implies that when the data is plotted; it is

symmetrically dispersed around the mean value of the data. The data for this study was normally

distributed as shown in the histogram graphs for normal distribution. The graphs show a normal

distribution in the bell curve for skewness and kurtosis. Morgan et al. (2001) stated that the

skewness and kurtosis statistics can be interpreted as symmetrical as long as they are between the

values of +1 and -1.

Figure 2. Histogram chart for the Personality variable.

Hair et al. (2006) stated that the Q-Q plot also determines the normality of data. If the

data plotted is along the normal line then the data is considered as normal.


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Figure 6.Normal Q-Q plot

Outliers

The assumption of outliers suggests that there should not be a unique or distinct response

from the rest of the data. It usually exists when there is one value on either of the extreme sides

of the x-axis and deviates from the other values of the sample (Field, 2005). This can be detected

by the z-score using SPSS (Brace, Kemp & Snelgar, 2006) and it should not go beyond the limit

of +2.5 and -2.5 (p


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Figure 10. Scatter plot diagram for the variables

In addition, the scatter plot matrix can also be used to visually represent the relationship of

variables that is shown in the figure 11.

Figure 11. Scatterplot Matrix for the Variables

Homoscedasticity

Homoscedasticity is assumes that the variance of all the dependent variables is somewhat

equal with all the independent variables. The scatter plot of the residuals of the regression


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analysis also shows the homogeneity of variances as long as they are equally spread along the

zero line.

Figure 12. Scatter plot graph of the Regression Residuals

Mulitcollinearity and Singularity

The assumption of multicollinearity and singularity tends to be violated, if there is found

a very high correlation among the independent variables in the correlation matrix. If the

correlation is very high (i.e. 0.90 or above) there exists the problem of multicollinearity however,

the problem of singularity is found if there is a perfect correlation among different variables of

the study. In this study, there is not found any problem of mulitcollinearity or singularity as all

the correlation values are less than 0.90 (see table 7). However, multicollinearity can be checked

by the tolerance value and variance inflation factor (VIF) obtained from collinearity matrix. Field

(2005) discussed that the tolerance value should be greater than 0.20 and VIF value sho uld be

less than 4 in order to avoid the problems of multicollinearity and singularity. The tolerance

values and VIF values for the variables of this study are shown in table 20. It shows that the

values of the collinearity statistics suffice the assumption of multicolinearity and singularity.

_assumptions of multiple regression analysis

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