Question

Real estate investors, home buyers, and home owners often use the appraised value of a property as a basis for predicting sale price. Data on sale prices and total appraised values (in thousand of dollars) of 92 residential properties sold in 1999 in an upscale Tampa, Florida, neighborhood named Tampa Palms are saved in the file – tampalms.dat.

To read the data into R, first save the data file onto a folly disk or to any local file. Then the following R codes basically read the data into a data.frame called tampalms.
tampalms <- read.table("tampalms.dat", header=F, col.names=c("appraised", "sale"))
First take the logarithm transformation on both X and Y and use them as the response and predictor.
x <- log(tampalms$appraised) y <- log(tampalms$sale)

Data is as follows:

170.432	180
212.827	245.1
68.13	85.4
65.505	87.9
68.655	84.2
64.98	85
67.605	81
100.861	125
108.981	124
102.523	126
104.203	128.5
102.681	127.5
105.175	128.2
80.954	107
101.515	125
89.119	116
102.066	122.5
89.588	118.9
106.118	120
147.865	188
158.26	183
161.309	195.5
162.395	193
151.475	192
203.826	256.9
222.012	270
214.728	230
259.848	332.5
217.125	310
220.041	230.5
228.806	257
253.876	300
205.529	275
318.508	365
202.127	258
263.847	279
286.744	340
324.578	335
266.542	297
140.743	166
151.305	187
148.115	163.4
182.272	59
170.863	221
270.04	290
235.087	260
348.574	445
302.133	406
136.315	185
116.446	176
133.912	171.1
153.25	182
127.93	166.5
306.172	295
298.68	369
289.489	350
315.663	365
320.017	390
348.574	365
352.985	440.3
112.242	100.3
225.613	220
150.348	187
169.282	214
171.832	185
156.224	182.5
144.384	165
139.94	167
127.706	160
111.856	130.9
125.731	160
128.329	142.8
615.586	560
572.523	715
140.04	176
164.849	178
125.187	156.5
149.202	153
422.913	528
372.377	475
330.554	427
929.396	957.5
192.105	260
201.886	262
159.705	154
223.001	260
179.056	215
195.862	244
176.85	219
95.718	132
137.108	156.9
183.704	263

5. Obtain the fitted values ^yi and residuals ri from the ftted model. Plot ri versus ^yi and comment.

Answer 1

Here, using R code, we are to obtain and . The R code for obtaining these are given below:
model=lm(y~x)
y_fit=model$fitted
res=model$resid
plot(y_fit,res,pch=16,main="Residual plot")

The residual plot is given below:

From the residual plot, we can see that the residuals are not symmetrically placed on either side of the "0" line. Also, we can see that there are outlier residuals present in the plot. This tells us that heteroscedasticity is present in the data set, meaning that the residuals get larger as the prediction moves from small to large (or from large to small).