# Linear regression analysis

#### Nomnso

##### New Member
Hi all,
I am having problems with analysis. I want to perform a multiple linear regression.
1). The dependent variable and all but one of the independent variables is normally distributed. I was made aware that the independent variables don't have to be normally distributed to use it for a regression but the residuals need to be normally distributed.
2). Second problem the fact that SPSS calculates pearsons r for the non normal variable instead of spearmans rho. Does this invalidate the analysis? Admittedly if spearmans correlation (one-tail.....I am told that is more accurate) is done between my dependent variable and my non-normal variable, the correlation is barely insignificant (p=0.056) but with peason (also one tail) it is very significant).
3). Any recommendation on the best way of checking for heteroscedasticity? I have looked at the scatter plot and it seems to have homoscedasticity and I have tried to test statistically by performing a linear regression using the square of the unstandardized residuals and checking that the ANOVA is not significant (not sure how that works). Is there any other means of checking?
See attached file for my output. Any help or suggestion would be highly appreciated

#### Attachments

• 475.4 KB Views: 7

#### hlsmith

##### Less is more. Stay pure. Stay poor.
What is your sample size?

#### noetsi

##### No cake for spunky
Second problem the fact that SPSS calculates pearsons r for the non normal variable instead of spearmans rho. Does this invalidate the analysis? Admittedly if spearmans correlation (one-tail.....I am told that is more accurate) is done between my dependent variable and my non-normal variable, the correlation is barely insignificant (p=0.056) but with peason (also one tail) it is very significant).
I don't think this is pertinent to the regression which uses OLS not spearman or pearson. Non-normality of the residuals is entirely separate from this. It does not matter if one variable is normal, it matters about the residuals of the regression.

While there are specialty tests looking at the graph is pretty much the normal way to test for this. If you are really concerned about this just use White's standard errors which effectively addressed this point. The other solutions like using weighted least squares are not simple and require information you may not have. In some cases logging or box cox may work, but I would just use White's SE its simpler.

If your sample size is large this probably will not be a major issue anyhow.

#### Nomnso

##### New Member
What is your sample size?
The total sample size is 116 but the problem is some of the variables have missing records and we dont want to exclude missing cases listwise because that makes us lose valuable input.

#### Nomnso

##### New Member
I don't think this is pertinent to the regression which uses OLS not spearman or pearson. Non-normality of the residuals is entirely separate from this. It does not matter if one variable is normal, it matters about the residuals of the regression.

While there are specialty tests looking at the graph is pretty much the normal way to test for this. If you are really concerned about this just use White's standard errors which effectively addressed this point. The other solutions like using weighted least squares are not simple and require information you may not have. In some cases logging or box cox may work, but I would just use White's SE its simpler.

If your sample size is large this probably will not be a major issue anyhow.
The total sample size is 116 but the problem is some of the variables have missing records and we don't want to exclude missing cases listwise because that makes us lose valuable input

#### noetsi

##### No cake for spunky
The total sample size is 116 but the problem is some of the variables have missing records and we don't want to exclude missing cases listwise because that makes us lose valuable input
You should look at the research on doing this. There are significant issues with doing what you are suggesting. They exclude cases like this for a reason (once I looked at the literature on this idea I abandoned the idea you suggest).

You should consider multiple imputations instead.