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Simple Regression Model

Simple Regression Model

Simple Regression Model

  1. Floor Area and Assessment Value Scatter Plot

There is a linear relationship between Floor Area and Assessment Value. The trend line and the regression equation indicate a positive linear relationship between the two variables (Rubinson, 2019).

Floor Area and Assessment Value Scatter Plot

Floor Area and Assessment Value Scatter Plot

  1. Whether Floor Area a significant predictor of Assessment Value
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.968358
R Square 0.937718
Adjusted R Square 0.935642
Standard Error 115.5993
Observations 32

 

ANOVA
  df SS MS F Significance F
Regression 1 6035852 6035852 451.6772 1.23E-19
Residual 30 400896 13363.2
Total 31 6436748
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 162.6628 54.47857 2.985812 0.005586 51.40269 273.9228 51.40269 273.9228
X Variable 1 0.306732 0.014433 21.2527 1.23E-19 0.277257 0.336207 0.277257 0.336207

 

Based on the regression analysis output of Floor Area and Assessment Value, the P-Value obtained (0.005586) is less than 0.05, which implies that the Floor Area significantly predicts Assessment Value.

  1. Age and Assessment Value Scatter Plot

The regression equation obtained shows no linear relationship between Age and Assessment Value.

Age and Assessment Value Scatter Plot

Age and Assessment Value Scatter Plot

  1. Regression Analysis of Age and Assessment Value
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.179004
R Square 0.032043
Adjusted R Square -0.00022
Standard Error 455.7228
Observations 32

 

ANOVA
  Df SS MS F Significance F
Regression 1 206249.6 206249.6 0.993097 0.326957
Residual 30 6230498 207683.3
Total 31 6436748
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1377.366 163.1906 8.440231 2.03E-09 1044.086 1710.646 1044.086 1710.646
X Variable 1 -5.59421 5.613615 -0.99654 0.326957 -17.0587 5.870325 -17.0587 5.870325

From the regression output, the P-value indicates that age significantly predicts the Assessment Value. However, due to the small R-squared value and the lack of linear relationship, age gives very minimal information about assessment value (Field, 2018).

  1. Multiple Regression Model for Assessment Value as the dependent variable and Floor Area, Offices, Entrances, and Age as independent variables.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.976236
R Square 0.953037
Adjusted R Square 0.946079
Standard Error 105.8108
Observations 32

The Overall R Square is 0.976236, while the Adjusted R Square is 0.946079

ANOVA
  Df SS MS F Significance F
Regression 4 6134458 1533615 136.9798 1.62E-17
Residual 27 302289.8 11195.92
Total 31 6436748
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 38.78345 77.09451 0.503064 0.618999 -119.401 196.9683 -119.401 196.9683
Floor Area (Sq. Ft.) 0.244041 0.025492 9.573045 3.59E-10 0.191735 0.296347 0.191735 0.296347
Offices 80.94592 35.65398 2.27032 0.031382 7.790001 154.1018 7.790001 154.1018
Entrances 86.59756 45.20452 1.915683 0.066051 -6.15446 179.3496 -6.15446 179.3496
Age -0.20799 1.406374 -0.14789 0.883528 -3.09363 2.677652 -3.09363 2.677652

Working with α=0.05, the predictors that can be regarded as significant predictors from the analysis output are the variables with a P-value less than .05. Therefore, the significant predictors are Floor Area and Offices with P-values of 3.59E-10 and 031382, respectively.

We can eliminate Age and Entrances since their P-values are greater than .05, which cannot be regarded as significant predictors.

To Obtain the Final model Using Floor Area and Offices as the predictors, we can generate another regression output with the two variables as shown below;

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.972788
R Square 0.946317
Adjusted R Square 0.942615
Standard Error 109.1571
Observations 32

 

ANOVA
  Df SS MS F Significance F
Regression 2 6091205 3045603 255.605 3.82E-19
Residual 29 345542.9 11915.27
Total 31 6436748
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 115.9136 55.82814 2.076257 0.04684 1.732186 230.0949 1.732186 230.0949
Floor Area (sq. Ft.) 0.264121 0.024012 10.99955 7.28E-12 0.215011 0.313231 0.215011 0.313231
Offices 78.33906 36.34622 2.155356 0.039569 4.002689 152.6754 4.002689 152.6754

Model: Y= 115.9136 + 0.264121X1 + 78.33906X2

Where Y= Assessed Value

            X1 = Floor Area

            X2 = Offices

Supposing our final model is:

Assessed Value = 115.9 + 0.26 x Floor Area + 78.34 x Offices; what would be the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?

By substituting the values in the model, we obtain;

Assessed Value = 115.9 + (0.26 x 3500) + (78.34 x 2)

= $1,182,580

Substituting the Floor Area and Offices values in the model for a building that was built 15 years ago, the outcome matches the value in the database, which implies the model is accurate.

References

Field, A. (2018) Discovering Statistics Using IBM SPSS Statistics, Sage Publishers, California.

Rubinson, C. (2019). Presenting Qualitative Comparative Analysis: Notation, Tabular Layout, And Visualization. Methodological Innovations12(2), 205979911986211. doi: 10.1177/2059799119862110

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Question 


Week 5 Simple Regression Model Spreadsheet

Assignment Content

Purpose

This assignment provides an opportunity to develop, evaluate, and apply bivariate and multivariate linear regression models.

Simple Regression Model

Simple Regression Model

Resources: Microsoft Excel®, DAT565_v3_Wk5_Data_File (See attached)

Instructions:

The Excel file for this assignment contains a database with information about the tax assessment value assigned to medical office buildings in a city. The following is a list of the variables in the database:

  • FloorArea: square feet of floor space
  • Offices: number of offices in the building
  • Entrances: number of customer entrances
  • Age: age of the building (years)
  • AssessedValue: tax assessment value (thousands of dollars)

Use the data to construct a model that predicts the tax assessment value assigned to medical office buildings with specific characteristics.

  • Construct a scatter plot in Excel with FloorArea as the independent variable and AssessmentValue as the dependent variable. Insert the bivariate linear regression equation and r^2 in your graph. Do you observe a linear relationship between the 2 variables?
  • Use Excel’s Analysis ToolPak to conduct a regression analysis of FloorArea and AssessmentValue. Is FloorArea a significant predictor of AssessmentValue?
  • Construct a scatter plot in Excel with Age as the independent variable and AssessmentValue as the dependent variable. Insert the bivariate linear regression equation and r^2 in your graph. Do you observe a linear relationship between the 2 variables?
  • Use Excel’s Analysis ToolPak to conduct a regression analysis of Age and Assessment Value. Is age a significant predictor of AssessmentValue?

Construct a multiple regression model.

  • Use Excel’s Analysis ToolPak to conduct a regression analysis with AssessmentValue as the dependent variable and FloorArea, Offices, Entrances, and Age as independent variables. What is the overall fit r^2? What is the adjusted r^2?
  • Which predictors are considered significant if we work with α=0.05? Which predictors can be eliminated?
  • What is the final model if we only use FloorArea and Offices as predictors?
  • Suppose our final model is:
  • AssessedValue = 115.9 + 0.26 x FloorArea + 78.34 x Offices
  • What would be the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?

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