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Use the data in KIELMC for this exercise.(i) The variable dist is the distance from each home to the incinerator site, in feet. Consider the modellog $($price$)=\beta_{0}+\delta_{0} y 8 l+\beta_{1} \log (d i s t)+\delta_{1} y 81 \cdot \log (d i s t)+u$If building the incinerator reduces the value of homes closer to the site, what is the sign of $\delta_{1} ?$What does it mean if $\beta_{1}>0 ?$(ii) Estimate the model from part (i) and report the results in the usual form. Interpret the coefficient on $y 81 \cdot$ log (dist). What do you conclude?(iii) Add $a g e, a g e^{2},$ rooms, baths, log(intst), log(land), and log(area) to the equation. Now, what do you conclude about the effect of the incinerator on housing values?(iv) Why is the coefficient on log(dist) positive and statistically significant in part (ii) but not in part (iii)? What does this say about the controls used in part (iii)?

(i) $\delta_1 > 0$, incinerator further away from more expensive houses (ii) See video. Coeff not significant. (iii) See video. (iv) The controls are necessary and they were omitted from (ii)

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part one by common sense. Houses further away from the incinerator should be worth more, so we should expect Delta one to be positive. If Beta one is also expected to be positive, then it means the incinerator was located. Father away from more expensive homes are to you. This is the estimated equation that a one hat is. There's estimation. Yeah, we can see that it has the expected positive sign, but it is not statistically significant. You can conclude about the significance of an estimate, an estimation by comparing it's standard error to its estimated magnitude. So in this case, Delta one hot as a standard error of 0.8 too much larger than its value of 0.48 and formerly we can. We can base our reason on the T start value. So the T start value. It's the ratio of the estimated coefficient, divided by its standard error. So in this case, it would be Delta one hat divided by the standard error of Delta one hat. And because we have the bottom part of the ratio is larger than the top part. So the T start is less than one. Yeah, whenever you see a T start smaller than one, the estimated result is not significant. Now let's come to Port Tree and four. We will add MAWR exponentially variable variables into the equation. These are all of them and what we can notice. Four later, one The coefficient of lack of distant between the home and the incinerators, we can see that it now becomes insignificant. It was significant in Part two before we add all extra variables. The reason is these extra variables are important to determine the value of the homes. But you did not include these variables in the in the regression, So the regression in Part two has a problem. It has a it has, Thea admitted. Variable bias and the bias is shown in the estimation for the lock of distance variable if you do further testing. If you look at the correlation between lock of distance and the extra variables, you can see that lack of distance is highly correlated with lot of the distance between the home and the interstate. Thank you and lock of land. So dropping these variables lock of interstate distance and lack of land from the equation. So it's a regression equation sold to include these two variables, it would cause a bias to lock of distance. The home that is located further away from their incinerator are also the ones further away from the interstate and has larger land. So when we drop these two variable from the regression, we win overstate the effect of the lack of distance of the distance between the home and the incinerator. That is a bias, and that is the reason why this variable is significant in Part two, but not significant in Part three.

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