# multivariate linear regression models.

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**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__

**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 wouldbe 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?

**Write **a 525-word report that includes the following sections:

Section 1

· Describe in detail if you observe a linear relationship between the 2 variables –FloorArea and AssessmentValue. Explain the significance of a linear relationship. Explain if FloorArea is a significant predictor of AssessmentValue and its significance. What is the Coefficient of Determination r^2 and its significance?

· Describe in detail if you observe a linear relationship between the 2 variables – Age and AssessmentValue. Explain the significance of a linear relationship. Explain if Age is a significant predictor of AssessmentValue and its significance. What is the Coefficient of Determination r^2 and its significance?

Section 2

· Explain in detail your analysis of the AssessmentValue as the dependent variable and FloorArea, Offices, Entrances, and Age as independent variables. What is the overall fit r^2 and its significance? 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:

AssessmentValue = 115.9 + 0.26 x FloorArea + 78.34 x Offices

(this is just an example…not your final model)

· Describe in detail 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? Explain why or why not?

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