Question 10.13

10.13 Assessment value versus sales price.

Real estate is typically reassessed annually for property tax purposes. This assessed value, however, is not necessarily the same as the fair market value of the property. Table 10.2 summarizes an SRS of 35 properties recently sold in a midwestern county.8 Both variables are measured in thousands of dollars.

hsales

  1. Inspect the data. How many have a selling price greater than the assessed value? Do you think this trend would be true for the larger population of all homes recently sold? Explain your answer.
  2. Make a scatterplot with assessed value on the horizontal axis. Briefly describe the relationship between assessed value and selling price.
  3. Based on the scatterplot, there is one distinctly unusual observation. State which property it is, and describe the impact you expect this observation has on the least-squares line.
  4. Report the least-squares regression line for predicting selling price from assessed value using all 35 properties. What is the regression standard error?
  5. Now remove the unusual observation and fit the data again. Report the least-squares regression line and regression standard error.
  6. Compare the two sets of results. Describe the impact this unusual observation has on the results.
  7. Do you think it is more appropriate to consider all 35 properties for linear regression analysis or just consider the 34 properties? Explain your decision.

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Table 10.3: TABLE 10.2 Sales price and assessed value (in thousands of $) of 35 homes in a midwestern city
Property Sales
price		 Assessed
value		 Property Sales
price		 Assessed
value		 Property Sales
price		 Assessed
value
1 83.0 87.0 13 249.9 192.0 25 146.0 121.1
2 129.9 103.8 14 112.0 117.4 26 230.5 212.1
3 125.0 111.0 15 133.0 117.2 27 360.0 167.9
4 245.0 157.4 16 177.5 116.6 28 127.9 110.2
5 100.0 127.5 17 162.5 143.7 29 205.0 183.2
6 134.7 127.7 18 238.0 198.2 30 163.5 93.6
7 106.0 110.9 19 120.9 93.4 31 225.0 156.2
8 91.5 90.8 20 142.5 92.3 32 335.0 278.1
9 170.0 160.7 21 299.0 279.0 33 192.0 151.0
10 295.0 250.5 22 82.5 90.4 34 232.0 178.8
11 179.0 160.9 23 152.5 103.2 35 197.9 172.4
12 230.0 213.2 24 139.9 114.9

10.13

(a) 30. Generally, this may be true because the sellers might expect buyers to “lowball,” but markets will vary. (b) The relationship is linear, positive, and strong. (c) House 27 has an assessed value of 167.9 but a sales price of 360.0. This observation is likely influencing the regression somewhat. (d) . (e) . (f) The outlier has some influence on the regression; particularly, the first model that includes the outlier has a much larger standard error than when the observation is removed.