Appraised Value Sale Price Note: Both values are in thousands of dollars. 170.43

Question

Appraised Value Sale Price Note: Both values are in thousands of dollars. 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 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 (y) and total appraised values (x) of 92 residential properties sold in 1999 in an upscale Tampa, FL neighborhood are located in the "tampalms" worksheet. Both values are in thousands of dollars. 4. a) b) c) d) Calculate and interpret the correlation between x and y Find the least squares estimates of the slope and intercept using R. Interpret the slope of the least squares line. Interpret the intercept of the least squares line. Does it have a practical meaning for this application? Explain e) Conduct a test of model utility using a -.05. f) Use the least-squares model to estimate the mean sale price of a property appraised at S300,000.

Explanation / Answer

a)

r = 0.97228

there is strong positive correlation between two variables

b)

first export the excel file

suppose y = sale price and x = appraised value

model = lm (y~x)

summary(model)

slope = 1.068725

intercept = 20.94193

c ) when we increased appraised value by 1 unit , then on average sale price increase by 1.0687 units

d)

when appraised value = 0 , then sale price = 20.94

no, it does not have practical meaning

e)

p-value = 1.35 * 10^(-58) <<< 0.05

hence the model is significant

f)

y^ = 20.94193415 + 1.068725111*x

y^ = 20.94193415 + 1.068725111*300

= 341.55946745

hence

341559.46745 $

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