Dear
I have an outcome (dependent) variable (scores received from a multiple-choice test/computerized reading comprehension test), and two predictors (independent variables) (the data received from two Likert-Scale questionnaires/Computer Familiarity Scale and Attitudes towards Computer Scale were transformed to continuous scales). I'm trying to probe the directionality of the effects i.e the effect of two independent variables on the dependent one. Moreover, the correlation among the variables should be assessed based on the results of coefficients determination (R2). I came to the solid conclusion that the Multiple Linear Regression may be the best statistical test to examine my research hypotheses. What’s your idea? is it the most appropriate test to run based on the aforementioned data? If yes, which assumptions should be met for running Multiple Linear Regression statistical test? Somebody says that the results of just two Normality and Durbin-Watson (absen of autocorrelation) are to be reported, and this is the accepted procedure for statisticians. But it seems that those two are not enough, and totally, 8 main assumptions should be met in this case, and the most important ones are .........
1. Linear relationship 2. Multivariate normality 3. No or little multicollinearity 4. No auto-correlation 5. Homoscedasticity.
Would you please inform me if I am required to meet all the assumptions for running Multiple Linear Regression test? or Not?
It is worth mentioning that I'm supposed to report the most appropriate, accurate and subtle results of statistical procedure in order to get the positive judgment of austere reviewers!
Thanks in advance
Warm Regards
Seyyed,
In a nutshell, here are the assumptions required to run MLR: (i) linearity of the independent variables with the dependent variable y ~ f(x1,x2, ..), (ii) independence of errors (no dependency among the independent variables), (iii) homoscedasticity or equal variance of errors across all levels of the independent variables, (iv) collinearity meaning the independnt variables are not correlated and finally (v) normality i.e. that the variables or errors are normally distributed.
Thanks for your constructive comments.
Actually I examined the normality of residuals by Kolmogorov-Smirnov test and checking normal P-P plot of regression standardized residuals. Then, the homoscedasticity was also examined by checking Scatterplot, and no tight or wide distribution of points was shown on both sides of the plot. In fact, two normal distribution and homoscedasticity assumptions were satisfied. Could the satisfaction of Linearity assumption be taken for granted if the aforementioned assumptions are met? Or I'm required to check the Linearity separately?
Then, absence of multicollinearity (the correlation between independent variables) was confirmed by the Variance inflation factor (VIF) value.
Finally, the 2.08 Durbin-Watson value confirmed that there was no autocorrelation (neither positive nor negative autocorrelation) between variables. That's all what I did.
I'll appreciate if you inform me of the appropriateness and accuracy of my procedure. Is there anything else I should do?
Regards
Hi Sir,
Multiple linear regression analysis makes several key assumptions:
- linear relationship
- Multivariate Normality
- No Multicollinearity
- Homoscedasticity
Would you please tell me if the relationship between the two DV and IV is linear based on the Scatterplot and points distribution?
What about this ?
Actually, I have moments of doubt to confirm the linear relationship between these two DV and IV due to the cone shape of the points distribution? I can't confirm the linearity based on this scatterplot! Are you in agreement? or have other ideas?
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