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Use the data in HPRICEl to estimate the model$$=\beta_{0}+\beta_{1} s q r f t+\beta_{2} b d r m s+u$$where price is the house price measured in thousands of dollars.(i) Write out the results in equation form.(ii) What is the estimated increase in price for a house with one more bedroom, holding squarefootage constant?(iii) What is the estimated increase in price for a house with an additional bedroom that is140 square feet in size? Compare this to your answer in part (ii).(iv) What percentage of the variation in price is explained by square footage and number ofbedrooms?(v) The first house in the sample has sqrft $=2,438$ and bdrms $=4 .$ Find the predicted selling price for this house from the OLS regression line.(vi) The actual selling price of the first house in the sample was $\$ 300,000$ (so price $=300$ ). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?

(i) $-19.32+0.128$ sqrft $+15.20$ bdrms(ii) $\$ 15,200$(iii). $\$ 33,120$(iv) 63.2$\%$(v) $\$ 353,544$(vi) From the above part, the estimated value of the home based only on square footage and numberof bedrooms is $\$ 353,544$ . The actual selling price was $\$ 300,000,$ which suggests the buyer underpaid by some margin. But, of course, there are many other features of a house (some that cannot even be measured) that affect price and have not been controlled in here.

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Chapter 3

Multiple Regression Analysis: Estimation

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Kidus S.

March 6, 2021

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Hi, everyone. Uh, this is the second computer exercise in Jeff Tree. He's a h price one, and we trained to estimate the model. The price is equal to beta zero parts. Better. One square fits better. Two bedrooms for you. So I just wondered Congressional State, huh? Regress price, square feet, bedrooms. And it gives me following estimates. My estimates are Well, I'm just gonna write out the resulting equation format in the question, so it's gonna be pretty cool, too. A 20 My estimate for bagels. You today's minus 19 3 15 Huh? 0.1 28 is my estimate for beta one square fit. And the estimate for beta to ISS 16 coins, 1 98 Okay, so this is 90 price heads comes up out of the regression. Okay, The second question is what is estimated increasing price for a house. Which one more bedroom holding square footage, constant. That is just the bedroom, like the coefficient on bedroom. And, uh, so this prices, this was in $1000. So if we have one more bedroom and keeping a square feet six, then it's just gonna be one time, 15 points. 1 98 right So when I say the change in price changing estimated cries. But one more bedroom is gonna be just coefficients Estimate Kokoshin times 2000 since the prices in $1000 and it's gonna be 15 points 1 90 times 1000 which is gonna be 15,000 longer than 98. All right, The third question is, what is the estimated increased in price? Her house with an additional bedroom with an additional bad room that is 140 square feet inside. So now we have an additional bad room. But we also have an additional 140 square. Fine. So the change in price is gonna be on 0.1 28 times 140 15 points 19198 times one and times 1000 can surprise is in $1000. And when we do this calculation, I'm just gonna call change in price. Second change in price. Let's call this one the first change in price. And as I said, it's gonna be 1000 times they don't want half times the changes square feet. I mean, which waas points 1 20 each times understand? 40 gonna be 15.1 98 times one and this gives me Turley tree point 1 18 So the estimated price change here is gonna be $33,000 and right. $118. $33,118. So? Well, okay, then we're gonna compare this to a 2nd 1 Why is this different? Because in the 1st 1 we're keeping the square feet thick and just increasing number bedrooms. So we were comparing the price of the house that is the same in square fits, but has formal bedroom and would expect an increase in price by more than 15,000 dollars. Andi, here we are comparing the results with four house that has that has one more bad room and has 140 square feet more in area size. Right? That is why those two are different than each other. The 4th 1 is what percentage of the variation in price is explained by square footage and then number off bathrooms. This just asked us the r squared that comes out from this regression and the r squared from this aggression is point 60 tree 19 so 63% off. The variation price is explained by square footage and the number of bedrooms. Okay. What afford part? The fifth part is the first house in simple has square state that is equal to 2400 and 38 has four bedrooms. Find the predicted selling price for this house from the orders of Russian life. So we're just gonna put these numbers in this equation here? Okay, so the predicted you in color, go back to Red to the predictive prize for this house and of the minus since the price he was in 1000 ton us again, to find the actual price, I have to multiply the result that I find by thousands she's gonna be minus 19 points to tweeted in, plus your points 1 28 times square pit, which is 2428 15 0.1 98 times the number of bedrooms, which is for and being the calculation that is this is gonna give me the result is gonna be creepy. Three points 5 21 So the estimated price of the house that has four bedrooms and a square foot has 2000 138th quest square foot is gonna be 353 thousands. Well, $521. All right. Okay. And the last part of this question is the actual selling price of the first house in sample of $300,000. Find it with the jewels, put his house. But it suggests that the bio underpaid overpaid for the house. So the actual price waas So the actual prize or $300,000 to find a residual, which is gonna So the jury is gonna be the actual price minus the estimated price. Right? And we usually no traditional by e. I guess it's gonna be price minus yes. Mated prize. Right. And the prices $300,000 and the estimated price we find it was damage $50,000. 53 thousands. 21 Yet So the difference is right. 53,000 $541. So from the model, the estimate was training 53,000 by the actual price was $200,000. So this bio actually under paid for the house would expect him patron and $52,000. This is our expectation on estimates. Total model The actual price of $20,000. So it is on the page. Thank you for watching hope. This helps

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