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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...
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.
References
Geisser, S. And Johnson, W.M. (2006). Modes of Parametric Statistical Inference, John Wiley & Sons.
____. (2012). Statistics Solutions. Retrieved http://www.statisticssolutions.com/academic-solutions/resources/directory-of-statistical-analyses/assumptions-of-multiple-linear-regression/#sthash.hirr3Y2x.dpuf
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