st: Indicator vs index

[Derya Karaci <dkaraci@yahoo.com>]

Dear all, 
Suppose there are three explanatory variables (1) an indicator - say 'dummy', and (2) a variable that takes the values of 0,0.5 and 1, say "index" (2) a continuous variable between 0 and 1 - say 'random'.  Suppose the first question is if the weather is bad or good, and the second one lets you choose between bad, mediocre and good, and the third one allows you to rate it between 0 and 1. All variables have an average of 0.5.  

I run a simple regression on, say your ice cream consumption "icr" (sorry for the example..). The coefficients turn out very different. In the example below, "reg icr dummy" has a coefficient of 15, meaning that moving from 0 to 1 increases your consumption by 15 kilograms. But "reg icr index" has a coefficient of 20....and "reg icr dummy" has a coefficient of 30. I am also adding this very simple data I used for illustration below. These coefficients make sense by looking at the data. But how to interpret them? Arethey comparable for interpretation purposes? Suppose going from bad weather to good weather, can I say icecreamconsumption increases by 15, 20 and 30 kilograms respectively, and allowing more information b/w 0 and 1 increases the predicted effect? In short, I want to get a sense of how the extra information between 0 and 1 helps me.  

Many thanks for any help! Any insight will be appreciated.


icrdummyindex  random
100.029977
200.031412
300.039247
400.101387
500.135224
600.178009
700.230841
800.244429
900.298035
1000.3097
110.5.317844
120.5.483295
130.5.48904
140.5.518647
150.5.519864
161.5.53802
171.5.539834
181.5.555991
191.5.593809
201.5.646822
2111.664031
2211.685778
2311.712493
2411.717916
2511.786182
2611.844232
2711.844532
2811.9128
2911.994404
3011.998831

Derya


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