# Linear regression with multiple variables in SPSS

Created the model with these variables:

• Dependent, scale: Total monthly income,

• Independent, scale: Members of household working,

• Independent, ordinal: Household head's monthly income (binned)

• Independent, nominal: Household head's employment status

From the nominal variable recoded these dummy variables:

• Dummy 1: Household head unemployed

• Dummy 2: Household head employed

• Dummy 3: Household head retired

I left out dummy 2 (employed) and expected the coefficients off dummy 1 to be negative but both dummy 1 and 3 is positive and big numbers but the significance levels are all ,000.

If I only do a regression analysis with total monthly income as dependent, and only with dummy variables as independent unemployed is negative as expected (-2372) and retired is (1910). But the significance levels are all over .05.

What I don't understand is how the significance levels are over .05 in the second case and ,000 in the first case. What am I doing wrong? Any help is much appreciated!

## 1 Answer

In fact, you didn't do anything wrong. I'll point out a few points and hope it will help you to better understand what's going on.

If I only do a regression analysis with total monthly income as dependent, and only with dummy variables as independent unemployed.

then the left out dummy2 treated as a benchmark, meaning you compare the dummy 1 average to the benchmark average. let's say $$Y_i = β_1 + β_2D_1i +β_3D_3i$$ what does this tell us? simply, the Mean Total monthly income for Household head employed (D2) is $$B_1$$

the Mean Total monthly income for Household head unemployed (D1) is $$B_1 + B_2$$

the Mean Total monthly income for Household head retired (D3) is $$B_1 + B_3$$

you just like using ANOVA (if the 3 categories), or a T-test if 2 categories.

in your first case, you are using ANCOVA ( ANCOVA models are an extension of the ANOVA models in that, they provide a method of statistically controlling the effects of quantitative regressors called covariates in a model that includes both quantitative and qualitative, or dummy, regressors).

the results from this mode could be different from those of second case (ANOVA one) But this should not be surprising, for in (ANOVA) we did not account for the covariate, differences.

I hope this will help you.