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7.3.4 Applications with Examples - IV

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    7.3.4 Applications with Examples - IV 7.3.4 Applications with Examples - IV
    Table of contents
    
    Introduction
    
    Data Overview
    
    Initial Model Development
    
    Comprehensive Regression Analysis
    
    Regression Results and Interpretation
    
    ANOVA Table Insights
    
    Further Statistical Measures
    
    Hypothesis Testing for Slope
    
    Residual Analysis
    
    Conclusion
    
    7.3.5 Applications with Examples - V
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    8.2.1 Macro Communication
    
    8.2.2 Micro Communication
    
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    8.2.4 Sales Promotions
    
    8.2.5 Developing Effective Ad Campaigns
    
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    8.2.7 Designing Marketing Communications
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    8.4.1 Personal Selling
    
    8.4.2 Sales Process in B2B Market
    
    8.4.3 Sales Process in B2C Market
  - 8.5 Sales Force Management
    8.5 Sales Force Management
    
    8.5.1 Designing Effective Sales Force
    
    8.5.2 Managing the Sales Force

7.3.4 Applications with Examples - IV¶

Introduction¶

Objective: Explore the application of simple and multiple linear regression to model selling prices of flats based on area in square feet and potentially other variables.
Context: Vijay Gowda, a real estate analyst working for Magic Bricks, uses a dataset from Jayalakshmi Puram in Mysuru to determine market rates for flats.

Data Overview¶

Dataset Characteristics: Consists of 30 observations including variables such as selling price, area (square feet), number of bedrooms and bathrooms, and features like premium locality, gated complex, and amenities.
Initial Analysis: Begins with a simple linear regression model focusing on area as the independent variable to predict selling prices.

Initial Model Development¶

Scatter Plot Analysis:
Reveals a rough linear trend but indicates potential outliers.
Trend Line Equation: \(y = 28.37 + 0.0968x\), where \(x\) is the area in square feet.
Coefficient of Determination (\(R^2\)): Initially found to be 0.44, suggesting moderate explanatory power.

Comprehensive Regression Analysis¶

Tool Used: Excel's Analysis ToolPak.
Regression Details:
Dependent Variable (Y): Selling price.
Independent Variable (X): Area in square feet.
Outputs to Generate: Regression results, residuals, standardized residuals, and their plots.

Regression Results and Interpretation¶

\(R^2\) Value Confirmation: Confirmed at 0.44 from Excel, aligning with the preliminary analysis.
Adjusted \(R^2\): Stands at approximately 0.43, consistent across models indicating the model's stability.
Standard Error: Noted at 70.57, representing an estimate of the standard deviation of the regression errors.

ANOVA Table Insights¶

SSR (Sum of Squares due to Regression): 111539.
SSE (Sum of Squares due to Error): 139462.
SST (Total Sum of Squares): 251001, with SSR accounting for about 44% of SST.

Further Statistical Measures¶

MSR (Mean Square Regression): Equal to SSR in this single-variable model at 111539.
MSE (Mean Square Error): Computed as 4981, based on 28 degrees of freedom.
F-Statistic: Calculated as 22.39, indicating the regression provides a significant fit to the data.
P-Value: Close to zero, strongly supporting the rejection of the null hypothesis (\(\beta_1 = 0\)).

Hypothesis Testing for Slope¶

Coefficient \(b_1\): Indicates a price increase of 0.09 lakhs (90,000) per square foot increase.
T-Statistic for \(b_1\): 4.73, with 28 degrees of freedom, suggesting significant impact of area on selling price.

Residual Analysis¶

Standardized Residuals: Some exceed \(\pm3\), potential outliers.
Residual Plots: Show randomness, supporting the model’s assumptions of homogeneity and independence.

Conclusion¶

Model Evaluation: Demonstrates a significant relationship between area and selling price, with room for model improvement by adding more variables.
Next Steps: Proposes developing a multiple linear regression model to include additional predictive factors, enhancing explanatory power and accuracy.

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