Use the data in HPRICEl to estimate the model =β0+β1 s q r f t+β2 b d r m s+u where price is the

step 1 Hi everyone. This is the second computer exercise in chapter 3. We're using the data H price 1 a

Use the data in HPRICEl to estimate the model =β0+β1 s q r f...

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 square footage constant? (iii) What is the estimated increase in price for a house with an additional bedroom that is 140 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 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. (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?

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 square
footage constant?
(iii) What is the estimated increase in price for a house with an additional bedroom that is
140 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 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.
(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?

Key Concepts

Interpretation of Regression Coefficients

Each estimated coefficient in a multiple regression represents the expected change in the dependent variable for a one-unit change in the corresponding independent variable, holding all other variables constant. This concept is critical to understanding how changes in individual factors, such as the number of bedrooms or square footage, affect the predicted house price.

Prediction and Residual Analysis

Prediction using an estimated regression model involves plugging the values of the independent variables into the estimated equation to obtain a predicted value for the dependent variable. The residual is the difference between the actual observed value and its predicted value, which helps in understanding the accuracy of the model and determining whether subjects, such as house buyers, paid more or less than the predicted market price.

Goodness-of-Fit (R-squared)

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables in the model. It is a key concept for assessing how well the model fits the data, indicating the level of explanatory power achieved by including variables such as square footage and the number of bedrooms.

Multiple Linear Regression Model

This concept involves constructing a linear equation that relates a dependent variable to two or more independent variables. It allows for the estimation of the impact that each independent variable has on the dependent variable. The general form of the model is written as Y = ?? + ??X? + ??X? + ... + u, where ?? represents the intercept, ??, ??, etc., represent the slopes or coefficients, and u is the error term capturing unexplained variation.

Marginal Effects

Marginal effects refer to the incremental impact of a change in an independent variable on the dependent variable. For example, the coefficient of the number of bedrooms shows how much the house price increases for one additional bedroom, assuming square footage remains fixed. This is central to accurately estimating and comparing the effects of changes in predictors.

Transcript

00:02 Hi everyone.

00:04 This is the second computer exercise in chapter 3.

00:08 We're using the data h price 1 and we're trying to estimate the model.

00:13 The price is equal to beta 0 plus beta 1 square fits plus beta 2 bedrooms plus you.

00:20 So i just run this regression of data.

00:24 It puts regress price square feet bedrooms and it gives me the following estimates.

00:32 So my estimates are, well, i'm just going to write out the result in equation format as if we're asking the question.

00:48 So it's going to be price is equal to beta 0.

00:55 My estimate for beta 0 is minus 19 .315 plus 0 .128 is my estimate for beta 1 square feet.

01:29 And the estimate for beta 2 is 15 .198.

01:45 So this is, right, price hat, what comes out of the regression.

01:56 Okay, so the second question is, what is the estimated increase in price for a house which one more bedroom holding square footage constant? that is just the bedroom, like the coefficient on bedroom.

02:19 And so this price since this was in thousand dollars so if we have one more bedroom and keeping a square feet fixed then it's just going to be one time 15 .198 right so let's say the change in price the change in estimated price with one more bedroom is going to be just coefficients, the estimate for coefficient times 1000 since the price is in thousand dollars and it's going to be 15 .198 times thousand which is going to be 15 ,000 and longer than 98.

03:25 All right.

03:29 The third question is what is the estimated increase in price for a house with an additional bedroom with an additional bedroom that is 140 square feet in size.

03:45 So now we have an additional bedroom, but we also have an additional 140 square fits.

03:54 So the change in price is going to be 0 .128 times 140 plus 15 .198 times 1 ,000, and times 1 ,000 ,000 times 1 ,000 times 1 ,000 ,000.

04:09 Prices in thousand dollars and when we do this calculation so i'm just going to call the changing price the second changing price let's call this one the first changing price and as i said it's going to be thousand times later one half times the change in square face variant which was point 128 times hundred and 40 plus it's going to be 15 .198 times one and this gives me 33 .18.

05:14 So the estimated price change here is going to be $33 ,000 and right, $118 .33 ,000.

05:35 So we'll okay then we're going to compare this to the second one.

05:40 Why is this different? because in the first one we're keeping the square feet fixed and just increasing a number of bedrooms.

05:48 So we were comparing the price of a house that is the same in square fits but has one more bedroom.

05:58 And we would expect an increase in price by more than $15 ,000...

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