Statistical assumptions and testing methods for multivariate regression analysis

¶ … Kolmogorov-Smirnof test

Factor analysis

Linear regression

Goldfeld-Quandt test

Kaiser-Meiyer-Oklin (KMO)

Multivariate regression

Correlation -- Pearson's r

Cronbach's ?

Durbin-Watson statistic

See descriptions and justifications below.

Correlation importance and justifications

Correlation measures the strengths of association between two variables and, as such, enables the performance of bivariate analysis ("Statistics Solutions, 2012"). The value range of the correlation coefficient extends between +1 and -1. A correlation coefficient of ± 1 indicates a perfect degree of association between the two variables. Assumptions for the Pearson r correlation include normal distribution, linearity, and homoscedasticity ("Statistics Solutions, 2012"). Linearity assumes a straight line relationship between each of the variables in the analysis and homoscedasticity assumes that data is normally distributed about the regression line ("Statistics Solutions, 2012").

7. Multicollinearity assumption & implication to student work

Multiple linear regression assumes little to no multicollinearity in the data. When independent variables are not independent from each other, multicollinearity exists ("Statistics Solutions, 2012").. There is also an assumption of independence regarding the error of the mean ("Statistics Solutions, 2012"). That is to say that the standard mean error of the dependent variable is independent from the independent variables ("Statistics Solutions, 2012").

8. Discuss ways to overcome the Multicollinearity

When multicollinearity occurs in the data, centering the data by deducting the mean score may be useful; however, this strategy generally works when the multicollinearity exists due to the application of non-linear transformations that have been used to correct missing multivariate normality ("Statistics Solutions, 2012"). A more robust method is to conduct a factor analysis before running the regression analysis, and then to rotate the factors to insure that the factors are independent in the factor analysis ("Statistics Solutions, 2012").

9. Discuss autocorrelation (serial correlation) assumption & implication to student work

Autocorrelation (lagged correlation or serial correlation) occurs when the correlation between values in a random process at different times that is a function of the time lag or of the two times ("Statistics Solutions, 2012"). That is to say that there is a relationship between a variable and itself over intervals of time ("Statistics Solutions, 2012"). These serial correlations occur in repeating patterns when the level of a variable at a time certain affects the variable at a future time ("Statistics Solutions, 2012").

10.Discuss ways to overcome the serial correlation

When using an estimated equation for statistical inference in hypothesis testing, the residuals will first be examined for evidence of serial correlation ("Statistics Solutions, 2012"). The Durbin-Watson statistic is a first order serial correlation that can be produced as part of the regression output ("Statistics Solutions, 2012"). The Durbin-Watson statistic measures the linear association between adjunct residuals from a regression model. It is basically the test of a the hypothesis p = 0 in the specification: ut = put-1+Et

11.Discuss homoscedasticity assumption & implication to student work

Homoscedasticity is generally considered the fourth assumption of multiple linear regression ("Statistics Solutions, 2012"). Homoscedasticity is equal statistical variation, and it can sometimes be ascertained on a scatter plot ("Statistics Solutions, 2012"). If the error terms along the regression line are all equal, the data is homoscedastic, such as shown in the data samples below ("Statistics Solutions, 2012").

12. Discuss ways to overcome the Homoscedasticity

To observe the occurrence of homoscedasticity, a test such as the Goldfeld-Quandt test can be used to show heteroscedasticity ("Statistics Solutions, 2012"). This test separates the high and low value data to see if the samples are significantly different ("Statistics Solutions, 2012"). While it is possible to correct for homoscedasticity in linear regression data, a non-linear correction can be applied; however, this can introduce multicollinearity into the statistical model ("Statistics Solutions, 2012").

13. Discuss statistics to be used to test model's variable; Justification for the selected statistical tests; Statistic(s) to be used to test models (overall); Justification for the selected statistical tests

See discussion items above.