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Why Should I Perform Pearson’s Correlation and Multiple Linear Regression Analysis?
By Steve Creech | February 26, 2011
Suppose you want to find out if there is a correlation between job satisfaction and the perception of the supervisor’s leadership style among non-supervisory employees. Suppose you use the Multifactor Leadership Style Questionnaire (MLQ) to measure five transformational leadership styles (the MLQ measures other leadership styles too but we don’t need them for this explanation). Let’s call the five leadership styles: L1; L2; L3; L4, and; L5. Let’s call job satisfaction “JS”.
So, why not just do one multiple linear regression analysis, put all five leadership styles (independent variables) into the model and whichever ones are statistically significant, those are the leadership styles that are correlated with job satisfaction? The answer is, it is possible for several independent variables to be individually correlated with a dependent variable, but not all of them will be statistically significant in the same multiple linear regression model.
Here is the idea, suppose the Pearson correlation statistic for comparing the five leadership styles with job satisfaction are: .29; .31, .38, .28, and .44, for L1, L2, L3, L4, and L5, respectively. Suppose that all five correlations are statistically significant. Now, when we put all five leadership styles in the same “multiple linear regression model”, the analysis shows that only L3, and L5 are statistically significant.
This would be important to know because it means that if all you have is one of the leadership style scores, that can be used to predict the dependent variable (job satisfaction). We can also see that if we had to choose, we would prefer to know L5, because it had the strongest correlation with job satisfaction. But if we wanted the best prediction model possible for predicting job satisfaction, we would know that we only care about L3, and L5. Once we know how much L3 and L5 leadership style a person has, knowing the amount of L1, L2, and L4 leadership style they have will not alter our prediction of the dependent variable.
In other words, all five leadership styles are correlated with job satisfaction, but not all five add up to collectively better predict the dependent variable. Only L3 and L5 “add independent information” about job satisfaction.
Topics: Dissertation Advice |
February 28th, 2011 at 6:22 pm
Good job…
March 20th, 2011 at 3:42 pm
Helpful. Clear and concise. Makes sense.
June 2nd, 2011 at 8:26 am
I just stumbled across your blog and it answered a whole handful of questions I needed to investigate in about 5 minutes flat. Thank you!
October 15th, 2011 at 8:39 am
Ah, excelent! I had this question in my mind for a long time. But what if in the regression appears an item that was non significant in the correlation?!is there a mistake or it can happen?!Actually, it happnes, but can you comment it?
October 16th, 2011 at 8:02 am
Regarding your question, Corina, I think if a variable X is not statistically significantly associated with another variable Y in a univariate analysis, but it becomes significant when other independent variables are accounted for in a multivariate analysis, it could be a correct finding or it could be a spurious result. I think multicollinearity or other mathematical problems (e.g. 0 cells, outliers, sample size too small etc) could sometimes cause this to happen. However, I think it is possible for a variable to become significant only when other variables are accounted for. For example, suppose there is a positive correlation between X and Y for males and a negative correlation for females. Then, when you look at only X and Y, the correlation cancels out. But, when you control for gender, the correlation shows up.