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Permalink Reply by Angshuman Saha on February 8, 2011 at 5:30pm

Hi Sarath,

For categorical variable like GENDER, linearlity means slightly different thing.

Let's say dependent variable PRICE is continuous and independent variable COLOR is categorical with 3 levels (red,green,blue).

Lets  talk about a model: PRICE = a + b*COLOR

In reality, the model is:   PRICE = a + b1 * I_green + b2 * I_blue

here I_green and I_blue are dummy (0/1) for those levels.

There is always 1 less dummy than # of levels. Here red is missing. That actually is called baseline.

So model is,

if COLOR =red , PRICE = a

if COLOR =blue , PRICE = a+b1

if COLOR =green , PRICE = a+b2

So, in this sense, PRICE is linear in COLOR. b1 and b2 are increase in price over and above the baseline color RED.

regards,

Angshuman

 

 

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Permalink Reply by Sharath Dandamudi on February 9, 2011 at 12:17am

Thanks a lot for the clarification Angshuman.I have one more question w.r.t. your response.In the example you provided let's say dummy variables I_Green and I_Blue don't turn out to be significant <hypothetical example,am not sure if this can happen.Please let me know if I am wrong>.Then, in this case, how will one know whether I_Red is significant or not?Hope my question is not silly :).

 

Thanks once again.

 

Regards,

Sharath

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Permalink Reply by Angshuman Saha on February 9, 2011 at 7:51pm

Hello Sharat,

   This is actually a good question. For a categorical variable, can the model say that some veles are significant, some levels are not. Typically after a regression we look at the ANOVA (Analysis of Variance) table. There we have 1 row per independent variable. In other words, in My example we will see a single row corresponding to the variable COLOR (as opposed to say 2 rows for I_green and I_blue). The F statistic for the COLOR variable, i nANOVA table will tell you whether COLOR - as a whole is significant or not.This is one way.

The other more complex way perhaps to dig deeper into data. Say I_green is significant but I_blue is not. That might mean - there is no significant difference in PRICE when you change COLOR from red to green. Howver when you change the COLOR to blue, there is a significant difference. In such a case you may redefine the COLOR variable with 2 categories ( red_or_green , blue). Refit the model and see if blue is now significant. So, what you are doing essentially is, merging two categories and calling in as one.

Typically in such cases, recommendation is, take a careful look at various exploratory plots and stats. For example, if you draw boxplot of PRICE, - one box per COLOR category - do you see that the boxes for red and green are pretty close and that for blue is very different? -- that kind of thing.

Regrads,

Angshuman

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Permalink Reply by Sharath Dandamudi on February 10, 2011 at 3:49am

Thank you Angshuman.

I am going to post one more question on a general topic.Your inputs and comments will be highly appreciated.

 

Regards,

Sharath

 

 

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Permalink Reply by Clifford Long on September 15, 2015 at 10:20pm

The 'linearity' assumption in linear regression means that the expected value of the response is a linear function of the parameters.   "Linear in the betas."  Compared to "linear in the predictor variable".  Here is more info  https://goo.gl/8YRr6A

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