Question

please show the steps and the code to solve this in R, thank you

11. (10 marks) (using dataset: "hpricel", in R: data(hprice1, package-wooldridge')) Use the data to 5 estimate the model where price is the house price measured in thousands of dollars iWrite out the results in equation form. iiWhat is the estimated increase in price for a house with one more bedroom, holding square footage and lot size constant? iii What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size, holding lot size constant? Compare this to your answer in part (ii) iv What percentage of the variation in price is explained by square footage, lot size and number of bedrooms? v The first house in the sample has lotsize-6126, sqrft-2438 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?

Answer 1

i) R code to estimate the model (all statements starting with # are comments and can be removed)

#Load the data hprice1
data(hprice1,package='wooldridge')
#print some records
head(hprice1)

#estimate the regression equation
fit<-lm(price~bdrms+sqrft+lotsize,data=hprice1)
summary(fit)

#get this

Call: lm (formula = price ~ bdrms + sgr ft + lotsize, data = hpricel) Residuals: 3Q Min 1Q Median Max -120.026 -38.530 -6.555 32.323 209.376 Coefficients: Cimate Std. Error t value Pr (>ItI) (Intercept)/-2.177e+0 2.948e+01-0.739 0.46221 1 . 385e+01、9. 010e+00 1 . 537 0 . 12795 bdrms 1.228e-01 1.324e-02 9.275 1.66e-14 sqrft 2.068e-03 6.421e-04 3.220 0.00182 ** lotsize Signif. codes: 0'***' 0.001 **0.01 '*0.05 '.' 0.1'' 1 Residual standard error 59.83 on 84 degrees of freedom Adjusted R-squared: 0.6607 p-value2.2e-16 Multiple R-squared: 0.6724, F-statistic: 57.46 on 3 and 84 DF

The estimated model is

price-一21.7703 + 13.8525 × bdrms+ 0.1228 × sqft + 0.0021 × lotsize

The estimated value of the slope coefficient for bdrms is 13.8525

This indicates that when the value of bdrms increase by 1, the price of the house increases by 13.8525 (in thousands of dollars), while holding sqrft and lotsize constant.

ans: The estimated increase in price for a house with one more bedroom, holding square footage and lot size constant is $13,852.5

iii) The estimated increase in price for one more bedroom is $13,852.5 from part ii).

The slope coefficient of sqrft is 0.1228. This indicates that for 1 square foot increase the price would increase by $0.1228 (thousands of dollars). The increase in the price for 140 square feet increase in the house area is 0.1228*140 = 17.1889 (in thousands of dollars)

The model is an additive. That means we can just add up the change in price due to increase in the number of bedrooms by 1 and due to which the increase in the total square feet by 140

ans: The estimated increase in price  for a house with an additional bedroom of 140 square feet in size holding lot size constant is 13,852.5+17,188.9=31041.5

In ii) we calculate the increase in price due to addition of 1 bedroom, while keeping the square foot of the house and the lot size the same, where as in iii) the price increase is due to an addition of 1 bedroom of size 140 square feet, due to which the total square feet increased by 140, while holding only the lot size the same.

iv) The value of r-square is (from the output)

R" = 0.6724

This indicates that 67.24% of variation in price is explained by square footage, lot size and number of bedrooms

v) The predicted selling price is

price--21.7703+ 13.8525 ×4+0.1228 × 2438+0.0021 × 6126 = 345.6398

ans: The predicted selling price is $345,639.8

R code

#predicted selling price
sp<-fit$coef[1]+fit$coef[2]*4+fit$coef[3]*2438+fit$coef[4]*6126
sprintf('The predicted selling price is $%.1f',sp*1000)
#or use this
sp<-predict(fit,newdata=data.frame(bdrms=4,sqrft=2438,lotsize=6126))
sprintf('The predicted selling price is $%.1f',sp*1000)

# get this

> #predicted selling price sp<-fitscoef[11+fitscoef [21 4+itscoef(31 2438+fitscoef(41 6126 > sprint f ('The predicted selling price is $.lf.spk1000) [1] "The predicted selling price is $345639.8" > #or use this > sp<-predict (fit , newdata-data, frame (bdrms-4 , sqrft-2438,10tsize-6126)) sprintf ('The predicted selling price is .1f', sp 1000) [1 "The predicted selling price is $345639.8"

vi) The fitted values for the data are stored in the variable fit$fitted.values.

The residual is actual - fitted value

R code

#calculate the residual for the first house in the sample
res<-300-fit$fitted.values[1]
sprintf('The residual for the first house in the sample is %.4f',res)

# get this

> #calculate the residual for the first house in the sample >res-300-fit$fitted.values [1] > sprintf ('The residual for the first house in the sample is . 4f",res) [1 "The residual for the first house in the sample is -45.6398"

The residuals are also directly stored in fit$residuals

R code

res<-fit$residuals[1]
sprintf('The residual for the first house in the sample is %.4f',res)

# get this

res<-fitsresiduals [1] > sprintf ('The residual for the first house in the sample is .4f', res) [1 "The residual for the first house in the sample is-45.6398"

The residual is negative. This indicates that the predicted price is higher than the actual price, that means the buyer has paid less than the price predicted by the model.

ans: The buyer has underpaid for the house.