Paper on Regression Analysis
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Project Paper Business Statistics
Bryant/Smith manual Case 28: We want to find an equation that gives the selling price of a house.
Things you'll want to do are:
1. Use regression analysis to derive a model of selling prices of houses in Eastville. Interpret your final model and its coefficients within the context of this problem. 2. Prepare a formula to use in predicting selling prices. Explain your formula in nontechnical terms. 3. Tell what additional information you'd like to have to predict the selling prices of these homes more accurately.
You will want to prepare a summary of your findings to present to a Board of Realtors. You should use a nontechnical discussion of your forecasting model.
Must include:
Explain why you chose a particular statistical methodology. Describe your assumptions. Show your statistical analysis. Give a correct statistical conclusion.
How to Organize the Report
I. The executive summary
A. Describe the most important facts and conclusions.
B. One paragraph, no more!
II. The introduction
A. Several paragraphs.
B. Contents
1.Background on the problem.
2.Questions of interest, problem statement, and/or hypotheses.
3.The nature of the data set - describe your sample.
III. Analysis and methods section
A. Interpret the statistical summaries
1.Tell the reader what you found in the data (results, facts only).
2.Explain what those findings mean with regard to the problem (interpret results).
B. Design - describe the most important aspects of how the data was collected.
IV. Conclusions and summary section.
A. What has the analysis revealed?
B. Why was the analysis done? (Refers back to your background.)
C. What of value was discovered? (Any unexpected results.)
D. How have your questions been answered? (Refers back to questions of interest, problem statement, and/or hypotheses
V. References
VI. Appendix
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Solution Summary
This posting provides a paper on regression analysis using data of selling prices of houses in Eastville.
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Project Paper Business Statistics
Bryant/Smith manual Case 28: We want to find an equation that gives the selling price of a house.
Things you'll want to do are:
1. Use regression analysis to derive a model of selling prices of houses in Eastville. Interpret your final model and its coefficients within the context of this problem.
Based on the Regression analysis using PRICE as the dependent variable and all the other factors as independent variables, the regression analysis was run to understand the drivers of Selling Price of houses in Eastville.
Regression Statistics
Multiple R 0.91
R Square 0.83
Adjusted R Square 0.81
Standard Error 11.59
Observations 108
ANOVA
df SS MS F Significance F
Regression 10 61703.81 6170.38 45.91 0.00
Residual 97 13037.83 134.41
Total 107 74741.64
Coefficients Standard Error t Stat P-value
Intercept -15.21 9.82 -1.55 0.12
SQ_FT 0.04 0.00 10.36 0.00
BEDS 4.92 1.96 2.51 0.01
BATHS -2.91 3.02 -0.96 0.34
HEAT -12.91 6.10 -2.12 0.04
STYLE 2.29 1.64 1.39 0.17
GARAGE 15.76 3.82 4.12 0.00
BASEMENT 9.08 3.45 2.63 0.01
AGE -1.03 0.28 -3.68 0.00
FIRE 5.31 3.98 1.33 0.19
APPLE VALLEY SCHOOL 4.62 2.53 1.82 0.07
The overall model is significant as the value of sig. F is less than 0.05 for the ANOVA table. The ANOVA table basically tests the hypothesis that overall model is significant i.e. Rsquare is not equal to zero. In this case, the value of Rsquare is 0.83 and Adjusted Rsquare is 0.81, which means that 81% of the variation in selling price of houses in Eastville is explained with the factors included in the Regression model.
The factors which have a P-value less than 0.05 are considered to be highly significant in influencing the dependent variable (Selling Price of Houses). In this model, the APPLE VALLEY SCHOOL variable is included in the model even though the P-value is more than 0.05 as the sample size of 188 is not very large and the P-value for APPLE VALLEY SCHOOL is very near to 0.05.
2. Prepare a formula to use in predicting selling prices. Explain your formula in nontechnical terms.
The formula for predicting selling prices of houses in Eastville, identified using Regression Analysis, is as follows:
Regression Model (Refer Excel sheet for details)
PRICE = 0.04 * SQ_FT + 4.92 * BEDS -12.91 * HEAT + 15.76 * GARAGE + 9.08 * BASEMENT - 1.03 * AGE + 4.62 * APPLE VALLEY SCHOOL
The coefficient means that for a variable if the value of the independent variable is increased by 1 unit, then the selling price of the house increases by the coefficient of the independent variable. For example: If the number of bedrooms (BEDS) is increased by 1, then the selling price of the house will increase by 4.92 (units used for selling price like $k). Similarly, for categorical variables ...
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