BUSI 444 Suggested Answers to Review and Discussion Questions: Lesson 7
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1 BUSI 444 Suggested Answers to Review and Discussion Questions: Lesson 7 1. Use Analyze Descriptive Statistics Descriptives to calculate the standard deviation and mean for each variable. Then manually divide the standard deviation by the mean to get the OV for each variable. Alternatively, you may use Analyze Descriptive Statistics Ratio to calculate the ratios between standard deviations and means, provided you are willing to create a new variable named UNITY (which should be equal to one) so that you have something to put in the Denominator field. The following tables show the OV statistics for SP_UNIT, SP_SQFT, and GIM. Ratio Statistics for SP_UNIT / UNITY oefficient of Mean entered 21.2% Variation Ratio Statistics for SP_SQFT / UNITY oefficient of Mean entered 26.5% Variation Ratio Statistics for GIM / UNITY oefficient of Mean entered 20.0% Variation The manual calculation of the OV should result in the same values as shown above. As can be seen, the GIM has the lowest OV followed by the SP_UNIT, and the SP_SQFT has the highest. Based on this test, the GIM should be selected as the most effective indicator. 2. Based on the answer to Question 1, GIM should be selected as the variable to model this approach. The factors that affect the GIM are very similar to those that affect the AP_RATE; therefore, in developing the model for GIM students should follow all the same steps as were covered in the lesson using GIM in place of AP_RATE. The only theoretical difference is that expenses may have an effect on GIM but not on AP_RATE, as AP_RATE uses net income after expenses. The first step is to state a general model for GIM. You needn't perform any caculations using this model, but you should keep it in mind so that you include all relevant variables in the SPSS model. GIM = b 0 + (b 1 * LOATION) + ( b 2 * AGE) + ( b 3 * units) + ( b 4 * SUITESIZE ) + ( b 5 * LANDRATIO ) + ( b 6 * AMENITIES) + ( b 7 * EXPENSES) As expenses were highly correlated with units, expense ratio (EXP_EGI) was used here. The following is the correlation report for 15 variables from our database (this report is limited to 15 variables due to space constraints you should consider many more):
2 Review Answer Guide: Lesson 7 Page 2 of 7 UNITS EFFAGE ONDITN DEPRE UND_PARK ELEVATOR AREA_UNT UNITS EXPENSES EFFAGE ONDITN DEPRE UND_PARK ELEVATOR AREA_UNT EXP_EGI NBHD NBHD NBHD STORY_ STORY_ SML_UNIT GIM EXP_EGI NBHD1 NBHD3 NBHD4 STORY_2 STORY_4 SML_UNIT GIM The report shows basically the same correlations as were shown for AP_RATE. To choose the variables to include in the model, observe which have the highest correlation with GIM. Among the variables you choose on this basis, you should ignore those that are highly correlated with each other. Here are the variables you might get from a first pass: UNITS EFFAGE ONDITN AREA_UNT NBHD1 NBHD4 STORY_2 STORY_4 SML_UNIT UND_PARK Of these, EFFAGE and ONDITN are highly correlated with each other, so you should choose just one of them. EFFAGE has a higher correlation with GIM than does ONDITN, so you should discard ONDITN. UNITS and SML_UNIT are also highly correlated with each other, so you should discard one of them. SML_UNIT has a higher correlation with GIM than does UNITS, so you should discard UNITS. Also, consider adding in NBHD3. It does not have as high a correlation with GIM as the other neighbourhood variables, but since all three were part of the same variable to begin with, we should add it to the list. This is where appraisal judgment comes into play the correlation data alone might lead you to leave it out, but good sense suggests you should leave it in. One area that was not included in the table, but that should probably be included in the model is LOT_AREA. Because it improved our model's predictive power when we used it in estimating capitalization rates, we can guess that it could have a similar effect here.
3 Review Answer Guide: Lesson 7 Page 3 of 7 You should now have something like the following list of variables: EFFAGE AREA_UNT NBHD1 NBHD3 NBHD4 STORY_2 STORY_4 SML_UNIT UND_PARK LOT_AREA The complete output for the final group selected is shown below. Although appraisal theory indicates that operating expenses or the expense ratio should be a factor in a GIM model, neither were found to be useful in this example. As noted above, EXPENSES was too highly correlated with UNITS to use and EXP_EGI was not well-related to GIM. 1 Variables Entered/Removed(b) Variables Entered UND_PARK, STORY_4, AREA_UNT, NBHD1, SML_UNIT, NBHD4, STORY_2, LOT_AREA, EFFAGE, NBHD3(a) Variables Removed Method. Enter a All requested variables entered. Summary R R Square Adjusted R Square Std. Error of the Estimate 1.961(a) a Predictors: (onstant), UND_PARK, STORY_4, AREA_UNT, NBHD1, SML_UNIT, NBHD4, STORY_2, LOT_AREA, EFFAGE, NBHD3 ANOVA(b) Sum of Squares df Mean Square F Sig. 1 Regression (a) Residual Total a Predictors: (onstant), UND_PARK, STORY_4, AREA_UNT, NBHD1, SML_UNIT, NBHD4, STORY_2, LOT_AREA, EFFAGE, NBHD3
4 Review Answer Guide: Lesson 7 Page 4 of 7 Unstandardized oefficients oefficients(a) Standardized oefficients ollinearity Statistics B Std. Error Beta t Sig. Tolerance VIF 1 (onstant) LOT_AREA AREA_UNT NBHD NBHD NBHD STORY_ STORY_ SML_UNIT EFFAGE UND_PARK a Dependent Variable: GIM This report shows a very high R 2 value, but there are 10 variables included. As there are only 30 sales here, this model should have no more than 6 variables. A step-wise process could be used to reduce the variable count to six. However, the three NBHD variables and the two STORY variables count as only one variable for each set, implying an overall variable count of 7 variables. Thus, removal of a STORY or NBHD variable would not have the desired effect of reducing the variable count, since removing only one of the binary variables would still leave the overall variable count at 7. Another method is to check the VIF or tolerance. The variables with the highest VIF or lowest tolerance are NBHD3 and UND_PARK. As removal of NBHD3 would not help, and removal of UND_PARK will reduce the variable count to an acceptable number, the report is re-run without UND_PARK. Variables Entered/Removed(b) Variables Entered Variables Removed Method 1 EFFAGE, STORY_2, STORY_4, NBHD4, NBHD1, AREA_UNT, SML_UNIT,. Enter LOT_AREA, NBHD3(a) a All requested variables entered. Summary(b) R R Square Adjusted R Square Std. Error of the Estimate 1.953(a) a Predictors: (onstant), EFFAGE, STORY_2, STORY_4, NBHD4, NBHD1, AREA_UNT, SML_UNIT, LOT_AREA, NBHD3 ANOVA(b) Sum of Squares df Mean Square F Sig. 1 Regression (a) Residual Total a Predictors: (onstant), EFFAGE, STORY_2, STORY_4, NBHD4, NBHD1, AREA_UNT, SML_UNIT, LOT_AREA, NBHD3
5 Review Answer Guide: Lesson 7 Page 5 of 7 Unstandardized oefficients oefficients(a) Standardized oefficients B Std. Error Beta t Sig. 1 (onstant) LOT_AREA AREA_UNT NBHD NBHD NBHD STORY_ STORY_ SML_UNIT EFFAGE a Dependent Variable: GIM This is a very good result. The adjusted R 2 is.866 and although the F-Ratio is only this is acceptable given the limited number of sales. NBHD3, NBHD4, and STORY4 have low T-values, but they do not add to the overall variable count, and all have at least a 70% probability that they are not equal to 0. Also, if the regression is re-run excluding each of these variables, the Standard Error of the Estimate increases, indicating that these variables have a beneficial effect in reducing error. However, the high significance percentages for these three variables indicate that they are the most likely to be removed by the stepwise process. The final step in the model building process is to analyze the results. The ratio of estimated to observed GIM is analyzed below (calculated by dividing the estimated GIM by the actual GIM). Note that these results should be identical to those that would be created by using the estimated GIM to create an estimated price and then using the estimate prices to create an assessment-sales ratio (ASR). If students used gross income to estimate price rather than effective gross income, this will create different values than those shown below, and is considered an error. Ratio Statistics for EST_GIM / GIM Mean % onfidence Interval Lower Bound.980 for Mean Upper Bound Median % onfidence Interval Lower Bound.972 for Median Upper Bound Actual overage 95.7% Minimum.859 Maximum Range.310 Price Related Differential oefficient of Dispersion The confidence interval for the median is constructed without any distribution assumptions. The actual coverage level may be greater than the specified level. Other confidence intervals are constructed by assuming a Normal distribution for the ratios. These statistics show an excellent result. The OD at 5.1% is close to the lowest acceptable value, since one can normally expect at least a 5% variation in ASRs as a result of sale price variations alone. The median is only slightly above 100% and the PRD is close to 1.00 showing no evidence of assessment bias.
6 Review Answer Guide: Lesson 7 Page 6 of 7 3. Step 3. Examine the potential independent variables for relationships with each other and with the dependent variable using graphic analysis, crosstabs and correlation analysis Graphic analysis 1. The main purpose of graphic analysis is to: Determine the nature of the relationship between the dependent variable and potential independent variables Determine if the relationship is sufficiently linear to meet the requirements of a linear regression model, or if the variables will required some transformation to capture a non-linear relationship Find the correlation between the dependent variable and potential independent variables a) You should review scatterplots b) You should review boxplots c) Frequency dstributions (rosstabs) 2. Frequency distribution is required to check for sales chasing problems If there are very few observations in a category, there is a tendency for the regression process to "chase" these sales. "hasing" sales is a term used to describe the process whereby the analysis will assign all of the residual value not explained by the main variable in the equation to the unusual characteristic. If you have nominal variables or binary variables in your dataset and you want to use them in your model, make sure you have sufficient observations to warrant a separate category. A general rule of thumb is to have at least 5 observations in each category. 3. orrelation analysis The key points on correlation analysis are: Assist in variable selection by finding the variables that are highly correlated with the dependent variable. This method is not always accurate, because some interval variables may not have the characteristics. orrelation analysis is primarily used to identify possible problems resulting from co linearity between the independent variables. (Multicollinearity) Interpreting correlation analysis: orrelations over 0.5 should be examined. orrelations do not usually create serious co linearity problems until they are over 0.8 Some of the correlations are misleading because of the small number of sales with the given characteristics. When a filter is used the correlation will increase.
7 Review Answer Guide: Lesson 7 Page 7 of 7 4. Risk: Risk is the chance that returns from investments will be less than the safe rate, say from a savings account or a GI. onsequently, risk is linked to the rate earned on a safe investment. In real estate, risk is lower for commercial or industrial properties leased to a reliable tenant, bur higher for a property leased to a weak tenant with a marginal business. Liquidity: Real estate investments are generally less liquid compared to stock, bonds or savings account, which can be cashed almost immediately. Selling real estate takes time and the cost are high (commissions). The absence of liquidity reduces the appeal of real estate as an investment or cause real estate investors to seek a rate of return higher than those for other investments. Investment management: Investment management is a decision-making process to safeguard the funds invested. Investment managers consider which investments should be bought and sold and when. Management requires though and planning based on factual knowledge and constant review of decisions. 5. Once the model is developed, it can be used to estimate GIM or ap Rate for unsold properties based on its unique characteristics. This is especially useful in areas where properties are heterogeneous. MRA makes more efficient use of sales data since various characteristics can be tested (for example, air conditioning, elevators, number of units, swimming pools and so on). When using MRA, unnecessary or redundant variables can be easily removed by using techniques such as Stepwise regression.
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