Bivariate regression, dummy variables and r^2

[Richard_R]

Hi all.

I am trying to find out if it's possible to calculate an r^2 value (% of variation explained) when performing a linear bivariate regression using dummy variables.

Let me provide an example of what I'm working on. I'm trying to find if a correlation exists between the type of house people live in and the amount of electricity they use, so my house types are:

Detached, semi-detached, terraced and flats.

I have monitoring data from several hundred houses and have worked out the average for each house type - let's suppose in terms of average kWh per year we have:

Detached - 4000 kWh/yr
Semi-detached - 3600 kWh/yr
Terraced - 3300 kWh/yr
Flats - 3200 kWh/yr

I've done ANOVA on the groups and found that there is a statistically significant differnce between at least two of them. My issue now is: how do I put these into a single equation that gives me some kind of r^2 value so that I can show how much variability is explained by the house type?

Is this even possible? How do I go about this?

Any advice greatly appreciated.

 

[Jhero]

ThanksYes, it is possible to calculate an r^2 value for a bivariate regression model using dummy variables. To do this, you will need to create a dummy variable for each house type, with the reference category being detached houses. Then, you can use the dummy variables in a linear regression model, and the coefficient for each dummy variable will tell you the difference in kWh/yr between that house type and the reference category. The R-squared value from this model will tell you how much of the variation in kWh/yr is explained by the house type.