# Thread: Help with OLS estimations

1. ## Help with OLS estimations

Hi, I have a problem I was doing OLS estimations on the data I gathered and I got strange result. I assumed that the price of house is affected by the area of the house and the year of building but here is what I've got

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 321325 81972 3.920 0.000135 ***
q5_y_du -5930 2227 -2.663 0.008601 **
q5_m_du 35496 2557 13.882 < 2e-16 ***

I'm not sure but in my opinion the intercept coefficient should be 0 as now it suggests that a new house with 0 m^2 costs 321325 or am I wrong and I should interpret it differently?

2. ## Re: Help with OLS estimations

The intercept term is computed so that the mean of the predicted values of dependent variable equals the mean the actual values of the dependent variable.

If you think that the intercept term should (theoretically) be zero, then rerun the regression and set (force) the intercept (constant) term arbitrarily to be zero. Note that, in so doing, the sum of the error terms of the regression model may not be zero. Thus, if you force both the intercept and the sum of the error terms to be zero, then the estimates of the regression weights for your model will not be (in general) unbiased.

3. ## The Following User Says Thank You to Dragan For This Useful Post:

dinomilka (02-05-2017)

4. ## Re: Help with OLS estimations

Originally Posted by Dragan
The intercept term is computed so that the mean of the predicted values of dependent variable equals the mean the actual values of the dependent variable.

If you think that the intercept term should (theoretically) be zero, then rerun the regression and set (force) the intercept (constant) term arbitrarily to be zero. Note that, in so doing, the sum of the error terms of the regression model may not be zero. Thus, if you force both the intercept and the sum of the error terms to be zero, then the estimates of the regression weights for your model will not be (in general) unbiased.
Thank you for the advice. So if I leave it (not to make it unbiased) how can I interpret that intercept? Simply should I say that it is the mean of the predicted values of house price?

5. ## Re: Help with OLS estimations

Originally Posted by dinomilka
Hi, I have a problem I was doing OLS estimations on the data I gathered and I got strange result. I assumed that the price of house is affected by the area of the house and the year of building but here is what I've got

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 321325 81972 3.920 0.000135 ***
q5_y_du -5930 2227 -2.663 0.008601 **
q5_m_du 35496 2557 13.882 < 2e-16 ***

I'm not sure but in my opinion the intercept coefficient should be 0 as now it suggests that a new house with 0 m^2 costs 321325 or am I wrong and I should interpret it differently?

In general, you need to look at a couple things to determine if you're able to interpret the intercept in OLS.
1) Is it logical to set all the independent variable values to zero?
2) Does your data set include observations for each independent variable where x=0 (or, better yet, is 0 within the min and max for each independent variable in the model)? For example, x-values ranging from negative to positive would cover this, even if zero wasn't actually observed.

You need to satisfy 1&2 for most cases to get a legitimate interpretation of the y intercept. Number 1 ensures that what you're doing is logical. Number 2 ensures that you're not extrapolating beyond your data set (it's possible the function is different outside of your relevant range; this applies to making predictions in general). Number 1 & 2 also tend to go hand in hand and can help you detect errors in your data. For example, if you check the high and low value for area of the house, and the min was a negative (or zero) value, you'd suspect that you input that observation wrong (and you know logically, a house with an area of zero or negative is nonsensical).

For these reasons, I wouldn't try to interpret the intercept as you've done (it doesn't make sense in this case). Additionally, I probably wouldn't jump to fitting the model without the intercept-- as mentioned above, some nice properties may be lost. Additionally, the usual R-squared doesn't mean the same thing when you fit the model without an intercept (another small caveat).

6. ## The Following 2 Users Say Thank You to ondansetron For This Useful Post:

dinomilka (02-05-2017), hlsmith (02-05-2017)

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