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).

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.

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 Innovations, 12(2), 205979911986211. doi: 10.1177/2059799119862110

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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.

Resources: Microsoft Excel®, DAT565_v3_Wk5_Data_File (See attached)

• DAT565_v3 Wk5 Data File

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?