Using data from 1988 for houses sold in andover...

Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and Mcclain (1995) , the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist): $$\begin{aligned} \widehat{\log (\text {price})} &=9.40+0.312 \log (\text {dist}) \\ n &=135, R^{2}=0.162. \end{aligned}$$ i. Interpret the coefficient on log (dist). Is the sign of this estimate what you expect it to be? ii. Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city's decision on where to put the incinerator. iii. What other factors about a house affect its price? Might these be correlated with distance from the incinerator?

Transcript

00:03 So, once again, i welcome to a new problem.

00:08 When you think about regression models for the most part, you typically have a linear regression model, and the linear regression model can be a simple linear regression model, or it could be a multiple linear regression model.

00:29 So your equation would have your x and your y variable, where your x is your independent and your y is your dependent and in this case what you see is if i had a table where the x was for example the age and then the y was the income then what's going to happen is that these are projection between age and income so each one of these points these are data points that you see.

01:05 So you have subjects, for example x1, x2, x3, and so on up until the nth one, where n is the sample size.

01:15 And then you also have y1, y2, y3 up until y n.

01:21 So these are those points representing the data points in the scatter plot.

01:30 And so if i have a projection, if i have a line, this is called the line of best feet, line of best feet.

01:40 And what's going to happen is i can come up with an equation showing the relationship between the dependent variable, which is x, age, and the dependent variable, which is y, for example.

01:57 That's what you're seeing right there.

01:59 And this is a regression model the slopes i'm gonna call the slopes blue which stands for the best linear and biased and biased estimator unbiased estimator so the beta 1 stands for the estimator which estimates the relationship between age and income so it estimates the relationship between age and income and so we can have quantitative relationships in this particular problem.

02:45 We can have quantitative relationships in this particular problem.

02:51 And for the most part, if your projection is non -linear, so for example if the x is non -linear, beta not plus beta 1 x1 if this is non -linear and then what's going to happen is we can log both sides of the equation so we can have a log on both sides so that it makes it a linear function so in our new problem we have data for house sales house sales in and the commonwealth of massachusetts so this is how to how sales so this is 1980 and this is 1980 and so we have an equation a log equation where the predictor or the predicted variable is the prize we have to log the price or price heart you see why i this is the price heart and it's a log because we want to make it linear and so this is the intercept 9 .0 and then the slope coefficient and then the log and so we're doing a comparison between the price and this is the price this is housing price this is housing price and this is housing price and this is is the distance from a garbage incinerator? so it's kind of like we're saying how will the distance from a garbage incinerator affect home prices.

04:53 So if this is our incinerator, this is d1 or rather this is, yes, distance one and then this is distance two and then the other one is going to be.

05:06 Distance three so we have all these distances so we want to see what this prize is going to be you know prize three prize two price one we want to see what what's going to happen with that also we're given the r coefficient being equivalent to sorry the r squared coefficient being equivalent to 0 .162 r squared is the coefficient of determination which reflects the relationship between the variation in relationship, variation in relationship between the distance, the distance and prize.

06:04 So we're looking at the variation of relationship between the distance and price.

06:10 And also the sample size for the number of whom is the same as 135 so that's what you're seeing with then the first question is interpret interpret the beta coefficient for log distribution so the beta coefficient for this one the point 312 and then explain the sign of the estimate.

06:50 So in this case we have a positive sign.

06:53 We want to explain that sign, the sign of the estimate.

06:58 The second question is confirm whether or not the simple regression provides unbiased estimator relating price to distance.

07:40 And this is based on the series planning choices, reflecting the location of the incinerator...

Question

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