# Interpreting parameter estimates when multicategorical predictors

I would like some advice on how to interpret parameter estimates with a continuous dependent variable (healthy food consumption) and a 6-category predictor (income, from 1 = lowest income to
6 = highest income band in GLM. My output is as follows:

Parameter Estimates
Dependent Variable: Healthy

$$\begin{array}{c|cccccc}&B&Std. Error&t&Sig.&Lower Bound&Upper Bound\\\hline Intercept& 7.578& 772&9.813&.000&6.059&9.097\\ [income=1]&-1.633 & .826&-1.977&.049&-3.259&-.008\\ [income=2]&-1.310 & .801&-1.635&.103&-2.886&.266\\ [income=3]&-.468 & .831& -.563&.574&-2.102&1.166\\ [income=4]&.664& .927 & .716&.474&-1.159&2.486\\ [income=5]&-.906 & .980& -.924&.356&-2.834&1.022\\ [income=6]&0^\rm a\end{array}$$$\rm a$. This parameter is set to zero because it is redundant.

If I plot income in a linear regression model as continuous, I get the following, but I'm not sure it's correct to do that: unstandardised coeff. (income) = .415, sig. = .000.

Which would be the best way to intrepret the results? For the first model (GLM), the only significant result I get is for income = 1, which is lowest income, and the B slope is -1.633. I'm not sure how to interpret that. If I would look at the second model (but not sure if it's correct to plot the categorical predictor like that in linear regression), it would suggest the higher the income is the more healthy food people eat. Thank you!

• It is better to use spaces, rather than tabs, to format your data on this site. – Chris Taylor Jan 24 '14 at 13:00
• Better still to use $\TeX$! Though on second glance, I may be stretching things a bit too much with this array...Anyway, I'd recommend penalized regression for an ordinal polytomous predictor like income bracket. – Nick Stauner Mar 27 '14 at 9:13