Management of a commerical real estate company wants to use a simple regression
ID: 3201713 • Letter: M
Question
Management of a commerical real estate company wants to use a simple regression model to explain assesesed value of comercial real estate property (Y) as a liner function of the property's floor space (X in sq. ft) In order to do so, they collect the following sample data. The have hired you as a management consutlant to correctly analyze the sample data. (file: assessed: text page 483)
1. In Excel, obtain the correct simple regression solution for this data (use =.05). [Note: you are required to replicate the Excel solution format of the provided course files on this topic.]
2. What is the correct simple regression equation in this case? Define the model parameters (intercept and slope) in this case.
3. Are the interval estimates of predicted property assessed value useful in this model (you are required to answer by correctly comparing commercial property 12 (A14) to commercial property 17 (A19)?
4. Is there any model shortcoming that is unique to either or both of the forecasted (fcst 16 & 17) assessed commercial property values? Explain in specific terms.
5. Referring to your Excel scatter plot with a fitted trend line, your Excel residual plot, the Excel normal probability plot, and the Excel standardized residuals for this model, are there any model shortcomings clearly apparent in this case (do the residuals appear to be a set of random numbers and approximately normally distributed and why must they exhibit these properties)? Explain in specific terms.
6. Explain in specific statistical terms why commercial property 8 (A10) has the least wide (most precise) prediction interval among the sampled properties.
PLEASE ANSWER ALL QUESTIONS.
commercial x= floor space y=assessed property in square feet value ($) 1 1280 671 2 1620 710 3 1820 678 4 2610 910 5 2930 950 6 2990 949 7 3570 1187 8 3660 1467 9 4720 1544 10 4790 1796 11 4880 1700 12 5000 1878 13 5650 1850 14 5720 1968 15 5942 2000 fcst 16 7000 fcst 17 5001Explanation / Answer
1. Ans:
The regression equation is
Y = 143 + 0.317 X
Predictor Coef SE Coef T P
Constant 142.64 75.54 1.89 0.082
X 0.31686 0.01843 17.19 0.000
S = 107.542 R-Sq = 95.8% R-Sq(adj) = 95.5%
Comment: The estimated p-values of intercept and slope (for X) are 0.082 and 0.000. Hence, we can reject the null hypothesis of slope at 0.05 level of significance and conclude that floor space in square feet has a significant effect on assessed value. Whereas, the intercept can not reject null hypothesis at 0.05 level of significance.
2. What is the correct simple regression equation in this case? Define the model parameters (intercept and slope) in this case.
Ans: The correct simple regression equation in this case
Y = 143 + 0.317 X
The intercept and slope of the model are 143 and 0.317. But the intercept does not have a significant effect. So, the model become
Y = 0.317 X
3. Are the interval estimates of predicted property assessed value useful in this model (you are required to answer by correctly comparing commercial property 12 (A14) to commercial property 17 (A19)?
Ans: Yes, the interval estimates of predicted property assessed value are useful in this model. The assessed value of property 12 is
Y = 0.317 *5000=$ 1585
While the assessed value of property 17 is
Y = 0.317 *5001= $1585.317. From both the result, we can see that the Y has a confidence interval.
4. Is there any model shortcoming that is unique to either or both of the forecasted (fcst 16 & 17) assessed commercial property values? Explain in specific terms.
Ans: No, there is only one model shortcoming that is unique to either or both of the forecasted (fcst 16 & 17) assessed commercial property values. Because for a given data set it has only one model.
5. Referring to your Excel scatter plot with a fitted trend line, your Excel residual plot, the Excel normal probability plot, and the Excel standardized residuals for this model, are there any model shortcomings clearly apparent in this case (do the residuals appear to be a set of random numbers and approximately normally distributed and why must they exhibit these properties)? Explain in specific terms.
Ans: From the above plots, we can see that the residuals appear as a set of random numbers and approximately normally distributed. If does not exhibit these properties on residuals our assumption on the model is violated. Because in regression we assumed that the residuals are followed an independent normal distribution with mean zero and variance sigma square.
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