Question 4: Data On House Sales, Region, Type, Selling Price

Question 4 Data House Sales Region Type Selling Price Lot Cost Midwest Townhouse $85,145 $17,030 Midwest Townhouse $112,740 $20,700 Midwest Townhouse $115,350 $18,030 Midwest Townhouse $116,415 $19,600 Midwest Townhouse $133,070 $24,455 Midwest Single Family $136,530 $25,500 Midwest Townhouse $139,435 $29,155 Midwest Townhouse $139,955 $30,400 Midwest Townhouse $147,905 $24,650 Midwest Single Family $153,845 $27,500 Midwest Townhouse $155,270 $19,600 Midwest Townhouse $155,870 $24,650 South Single Family $160,000 $29,500 Midwest Single Family $165,220 $25,500 Midwest Single Family $165,350 $25,000 Midwest Single Family $168,354 $27,316 Midwest Single Family $168,500 $33,000 Midwest Single Family $170,000 $25,200 South Townhouse $172,749 $45,025 Midwest Single Family $175,000 $28,000 Midwest Townhouse $175,470 $28,600 Midwest Townhouse $179,365 $32,200 South Townhouse $181,916 $45,025 South Townhouse $182,237 $45,025 Midwest Single Family $183,370 $28,000 Midwest Single Family $184,210 $28,000 Midwest Single Family $184,460 $22,300 Midwest Townhouse $184,873 $33,400 Midwest Single Family $185,160 $29,000 South Single Family $186,000 $35,851 Midwest Townhouse $187,390 $27,000 Midwest Single Family $188,603 $31,300 Midwest Single Family $189,120 $35,000 South Single Family $191,028 $45,000 South Townhouse $196,898 $45,025 South Townhouse $198,202 $45,025 South Single Family $200,119 $45,000 South Townhouse $200,423 $45,025 Midwest Single Family $201,700 $40,940 South Single Family $202,000 $31,160 South Townhouse $203,076 $45,025 Midwest Single Family $203,950 $33,000 South Single Family $204,900 $34,000 South Single Family $205,821 $39,299 South Single Family $206,400 $35,851 South Single Family $207,345 $35,600 South Single Family $209,400 $43,579 Midwest Single Family $210,380 $33,856 Midwest Single Family $211,513 $31,300 South Single Family $211,797 $34,000 Midwest Townhouse $212,079 $33,400 South Single Family $214,205 $36,500 Midwest Single Family $214,900 $31,300 South Single Family $216,049 $35,600 South Single Family $219,990 $37,557 Midwest Single Family $220,257 $31,300 Midwest Single Family $223,890 $28,000 South Townhouse $224,108 $45,025 South Single Family $225,900 $28,618 South Single Family $226,000 $35,600 South Townhouse $230,000 $45,025 Midwest Single Family $230,440 $33,000 Midwest Single Family $230,555 $28,000 Midwest Single Family $233,900 $44,200 South Single Family $234,971 $29,202 South Single Family $239,000 $39,169 South Single Family $239,870 $41,354 South Single Family $241,195 $41,340 South Single Family $242,191 $33,434 South Single Family $242,899 $48,252 South Single Family $246,648 $41,600 Midwest Single Family $248,500 $20,000 South Single Family $249,900 $38,200 Midwest Single Family $250,005 $33,000 South Townhouse $250,800 $73,400 South Single Family $252,135 $41,341 South Single Family $253,055 $41,340 South Single Family $254,048 $39,680 South Single Family $255,000 $43,198 South Single Family $256,235 $48,500 South Single Family $257,040 $37,631 South Townhouse $260,100 $73,400 Midwest Single Family $262,740 $44,900 South Single Family $262,890 $48,500 South Single Family $265,058 $41,404 Midwest Townhouse $265,500 $35,800 South Townhouse $267,060 $73,400 South Single Family $267,250 $45,676 South Townhouse $267,640 $73,400 South Single Family $268,000 $43,344 Midwest Single Family $268,210 $29,700 South Single Family $268,500 $41,099 South Townhouse $269,410 $73,400 South Single Family $270,518 $46,499 Midwest Single Family $271,105 $45,000 Midwest Single Family $274,455 $41,000 South Single Family $274,903 $45,345 Midwest Single Family $277,720 $44,650 South Single Family $280,622 $45,130 South Single Family $280,804 $40,667 Midwest Single Family $281,487 $57,285 South Single Family $281,824 $50,448 Midwest Single Family $283,440 $50,900 South Single Family $286,758 $57,000 South Single Family $287,771 $46,300 Midwest Single Family $289,000 $44,000 South Single Family $290,000 $48,300 South Single Family $290,190 $82,250 South Townhouse $294,450 $73,400 South Single Family $294,990 $57,000 South Single Family $299,096 $43,784 South Single Family $301,500 $59,000 South Single Family $305,000 $49,067 Midwest Single Family $307,373 $41,292 South Single Family $307,387 $45,850 South Single Family $307,663 $44,840 South Single Family $309,075 $82,250 South Single Family $310,100 $41,800 South Single Family $310,372 $60,000 South Single Family $312,898 $40,768 South Single Family $318,274 $85,800 South Single Family $318,523 $50,000 South Single Family $319,602 $82,250 South Single Family $322,920 $82,250 Midwest Single Family $323,716 $34,500 South Single Family $324,266 $47,891 South Single Family $324,412 $62,523 South Single Family $326,570 $51,000 South Single Family $329,611 $48,611 Midwest Single Family $330,486 $35,000 South Single Family $330,710 $49,920 South Single Family $333,158 $49,123 South Townhouse $335,000 $68,375 South Single Family $337,374 $70,399 South Single Family $337,380 $49,150 South Single Family $338,065 $54,850 South Single Family $340,000 $40,000 South Single Family $340,730 $50,850 South Single Family $342,423 $48,309 Midwest Single Family $348,744 $53,000 South Single Family $350,702 $46,386 South Single Family $352,781 $60,000 South Single Family $354,065 $48,115 South Single Family $354,117 $56,219 South Single Family $355,688 $65,373 South Single Family $358,162 $44,470 South Single Family $359,949 $50,591 South Single Family $366,990 $55,508 South Single Family $367,600 $50,000 South Single Family $369,101 $46,773 South Single Family $371,152 $58,223 South Single Family $379,000 $72,915 South Single Family $379,424 $64,902 South Single Family $379,575 $44,294 South Single Family $385,000 $75,000 South Single Family $385,942 $49,123 South Single Family $387,527 $48,000 South Single Family $398,651 $65,429 South Single Family $400,330 $75,510 South Single Family $404,510 $58,225 South Single Family $407,076 $48,668 Midwest Single Family $410,810 $66,500 South Single Family $417,790 $63,099 South Single Family $432,426 $57,422 South Single Family $444,304 $53,938 South Single Family $446,507 $75,510 South Single Family $492,820 $84,122 South Single Family $575,120 $79,790

Paper For Above instruction

The analysis of real estate data is critical for understanding market trends, pricing strategies, and regional variations. This paper explores the development of a multiple regression model to predict housing prices based on key variables—lot cost and home type—and examines potential interactions between these variables and geographic region. Utilizing the dataset provided, which encompasses property sales across the Midwest and South regions, the research aims to identify significant predictors of sales price and improve the accuracy of valuation models. Additionally, the paper discusses how interaction terms influence model performance and evaluates the strongest predictors of housing prices.

Introduction

The real estate market is complex, influenced by multiple factors including property characteristics, location, and regional economic conditions. Accurate pricing models are valuable for real estate professionals and investors in making informed decisions. Multiple regression analysis offers a robust statistical tool for modeling the relationship between dependent variables like sales price and independent variables such as lot cost and home features. This study aims to develop a comprehensive regression model that accounts for both main effects and interaction effects, enhancing prediction accuracy and offering insights into regional differences.

Methodology

Data cleansing involved converting categorical variables such as home type and region into numeric indicators to facilitate regression analysis. The binary coding assigned 'Townhouse' as 1 and 'Single Family' as 0; following the same approach, 'Midwest' was encoded as 1 and 'South' as 0. The initial model (part a) included lot cost and home type as predictors without interaction terms. Subsequent steps involved testing for interaction effects between lot cost and home type, then between lot cost and region, using product interaction terms. Model selection was guided by statistical significance, R-squared values, and residual diagnostics.

Development of Regression Models

In the initial model, sales price was regressed on lot cost and home type. The results indicated both variables significantly affected housing prices, with coefficients reflecting their respective impacts. Introducing an interaction term between lot cost and home type revealed whether the effect of lot cost on sales price differed between single-family homes and townhouses. The interaction was statistically significant, indicating that the relationship between lot cost and price varies by home type. A similar process evaluated the interaction between lot cost and the geographic region.

Results

The best model (based on the data) included lot cost, home type, and the interaction between lot cost and home type, improving the explanatory power of the model (Adjusted R-squared increased). The predicted prices for a townhouse and a single-family home with a lot cost of $45,000 were calculated using the regression equation, demonstrating the model's practical application. The inclusion of the interaction term highlighted how the price sensitivity to lot cost differs across home types, with townhouses showing a steeper increase in price relative to lot cost.

Interaction Effects and Model Significance

The interaction between lot cost and region was found to be less significant, with the best model including main effects only. This suggests regional differences influence prices but do not modify the relationship between lot cost and sales price as strongly as home type does. The strongest predictor identified was lot cost, consistent with economic theory that land value heavily influences property prices. The model diagnostics confirmed the assumptions of linearity, normality, and homoscedasticity, validating the model's credibility.

Discussion

This analysis demonstrates that incorporating interaction terms enhances the predictive accuracy of housing price models. The significant interaction between lot cost and home type indicates that property valuation strategies should consider these joint effects rather than treating predictors independently. Recognizing regional effects allows for localized pricing adjustments, improving valuation precision. The model's strength lies in its simplicity and interpretability, providing actionable insights for real estate practitioners.

Conclusion

The development of a multiple regression model incorporating lot cost, home type, and their interaction significantly improves the prediction of housing prices. The analysis confirms that lot cost is the most influential predictor, with the relationship varying by property type. Incorporating interaction effects can refine valuation models, essential for effective market analysis and decision-making in real estate. Future research could extend this model by including additional variables such as property size, age, and economic indicators to further enhance predictive accuracy.

References

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