# Solved Assumptions of Linear Regression [duplicate]

I am a bit confused with this.

Independence - The response variables are independent. I only have a single response variable so OK? Or observations are independent of each other? E.g Auto Correlated

Normality - The response variable is normally distributed. My response variable (Y) fails a number of normality tests, so not OK. Do I transform to meet this assumption?

Homoscedasticity. - Same variance. Not sure how to test this. Is this part of residual examination? The linear model i am proposing has 4/5 explanatory variables, how do i determine this?

Linearity - Straight line. Well when plotting Y and all X's separately, some are loosely linear. Should I be testing non-linear functions? How do I determine which to use?

I dont have a great deal of time, but I am not comfortable with the current model I am using.

Any help would be great, thank you

• I've noticed your flag to delete this question. I don't think we need to delete the whole thread, especially given the fact an answer has been upvoted and accepted. – chl Apr 4 '13 at 11:33
• As with just about any basic introductory statistics question (i.e. an issue that is covered any introductory statistics class), this has been answered multiple times on this site before - e.g. What is a complete list of the usual assumptions for linear regression?. Please consider taking a minute to search the site before asking/answering questions like this (finding this duplicate took approx 30 seconds), as cluttering the site with duplicates does no one any good. – Macro Apr 4 '13 at 12:10

These are not correct. Where did you get them?

Independence - There is only one responses variable. But the data have to be independent. For more on this see my blog post: Dependent and independent data

Normality - The thing that has to be normally distributed is the residuals from the model, not the response variable.

Homoscedasticity. - This does mean same variance. It can be examined graphically. This is easy in SAS and R and probably other programs. What program are you using?

Linearity - Regression only tests the strength of linear relationships. For more about this, search this site and elsewhere for terms such as linearity, regression and transformation. You can also examine this graphically by looking at plots.

I also suggest that you get a good basic text on regression. There are many such, choose one that uses examples from your field and that has an appropriate level of math for you.

• Thank you.From some online material for a masters of applied statistics course. – Will Apr 4 '13 at 10:25
• The residuals are not normally distributed... – Will Apr 4 '13 at 10:27
• Then you can look into transformations of the dependent or independent variable; or methods other than OLS. – Peter Flom - Reinstate Monica Apr 4 '13 at 10:44
• The residuals not being normally distributed is not necessarily bad thing and not and in large samples not an assumption by itself. – Majte Apr 4 '13 at 13:28