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Introductory Econometrics Econometrics (4th Edition)
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Chapter Cha pter 3, Problem 2CE
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Use the data data in HPRICE1.RAW HPRICE1.RAW to estimate the model model price = β0 + β1sqrft + β1sqrft + β2bdrms β2bdrms + u, where price is price is the house price measured measured in thousands of dollars. dollars.
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(i) Write out the results in equation form. (ii) What is the t he estimated incr ease ease in price for for a house with one with one more bedroom, bedroo m, holding square footage constant? (iii) What is the estimated increase in price for a house with an additional bedroom that is 140
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square feet in size? Compare this to your answer in part (ii). By providing your phone number, you agree to receive a one-time automated text message with a link to get the app. Standard messaging rates may apply.
(iv) What percentage of the variation in price is explained by square footage and number of bedrooms? (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.
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(vi) The actual selling price of the first house in the sample was $300,000 (so price = 300). Find he residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
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(i) The estimated model is written below:
The required estimated model can be obtained in Minitab by using below steps: 1. Go to Stat > Regression > Regression as shown in the below screenshot:
Comment
Step 2 of 9
2. The below dialog box opens. Enter the required variables corresponding to “Response” and “Predictors” headings. The updated dialog box is shown below:
Comment
Step 3 of 9
3. Click OK to get the below output:
The estimated regression equation is:
With:
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Step 4 of 9
(ii) Holding square footage constant, the above equation can be written as:
So,, est So estim imat ated ed pr pric ice e inc incre reas ases es by 15 15.2 .20 0 whi which ch me mean ans s
beca be caus use e pri price ce me meas asur ured ed in
housands of dollars.
Comment
Step 5 of 9
(iii) The equation given in part (i) is given below:
Here,
Therefore,
Comment
Step 6 of 9
So,, est So estim imat ated ed pr pric ice e inc incre reas ases es by 33 33.1 .12 2 whi which ch me mean ans s
beca be caus use e pri price ce me meas asur ured ed in
housands of dollars. Because the size of the house is increasing, this is a much larger effect han in (ii).
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Step 7 of 9
(iv) Since
, about
of the variation in price is explained by square footage and
number of bedrooms.
Comment
Step 8 of 9
(v) The equation given in part (i) is given below:
Here:
Therefore, the predicted price can be calculated as shown below:
The predicted price is
.
Comment
Step 9 of 9
(vi) From the above part, the estimated value of the home based only on square footage and number of 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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