# Confusion over interpreting regression coefficients

My lecturer's regression:

Variables:
*lprice*, the log of house prices
*y81*, which is a dummy for the year 1981 against 1978
*ldist*, log of distance from incinerator to houses


These are comments made by my lecturer to help give context:

• From the lecture we know that in 1978 people did not know about the incinerator site.
• By 1981 people did know about the site.
• If building the incinerator reduces the value of houses closer to the site, the coefficient on y81*ln(dist), delta_1, will be positive.
• If beta_1 is positive it indicates that the incinerator is being located in an area where the houses are of lower value.
• (If politicians/planners assume that poorer people have less lobbying power, this would be evidence of strategic decision-making on their part.) After regression was done my lecturers comment was this:

• The coefficient on y81ldist is positive, but small and not significantly different from zero at the 10% level (or the 5% level or the 1% level).
• In contrast the coefficient on ldist is positive and significant at the 0.1% level according to a two-tailed test.
• Based on this preliminary analysis, I conclude that the incinerator has no effect on house values.

Now i changed lprice to price to see if it made a difference. Here is the regression I got: Here the coefficient of y81ldist is quite large, and significant at 6.7% level, compared to a 55% in the first regression.

Im curious as to why my lecturer concluded that building the incinerator had no effect on prices? Am I overlooking something? From my regression, it shows that building the incinerator reduced prices of houses that are nearer to it by an average of ~15,400 dollars. (Also, does the 19302 coefficient on ldist mean that before the incinerator was built, prices of houses that were further away from the proposed site of building were already 19302 dollars more expensive that the ones closer?)

Are my interpretations right? Any insight would be appreciated.

## 1 Answer

Yes, you are correct with your interpretations. However, I think that your mistake could have probably came from the fact that you used "$price$" instead of "$\ln(price)$", which might have led to some violation of the normality and homoskedasticity assumptions of the linear regression model. Since you are inferring about the relationships between your predictor and price, assumptions must be met by your model (hence your variables). In that matter, to give you the mathematics of it, the p-value (which in your case, the one which is valued 6.7%) was calculated using the t-distribution. This heavily relies on the assumption that your dependent variable follows a normal distribution, since this would then imply that the slope coefficient $\beta$ will follow a t-distribution. Maybe you can look into some introductory books for linear models to verify this.

• Welcome to the site. I've edited your question to fix some grammar issues. – mpiktas Dec 27 '13 at 7:39
• Thanks a lot for this answer math_stat! how should I ideally go about checking if my dependent variable follows a normal distribution? I have both STATA and R installed. – Siddharth Gopi Dec 28 '13 at 1:41
• Also, i would like to know if youre calling my functional form a mistake, based on the premise that my lecturer concluded there is no relationship between the incinerator and house prices. (In other words, is it generally wrong to use variables that take values in thousands at levels? Or is there some possibility that using prices instead of lnprices was better in this case?) – Siddharth Gopi Dec 28 '13 at 2:49
• I am not so sure with both programs since I use SAS. I would assume that maybe under variable descriptives there is an option for Shapiro-Wilk's Test to check for Normality. As to your functional form, it is not wrong. As a matter of fact, you can have it that way but the only problem is you cannot do inferences on relationships unless you have checked for the assumptions. In that sense, your functional form is acceptable if the sole purpose of the model is to predict values, not infer relationships. :) – math_stat_enthusiast Dec 28 '13 at 16:35
• alright, thank you very much! that was something important that i didnt know about until now! – Siddharth Gopi Dec 29 '13 at 3:27