Using Regression Analysis

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Using Regression Analysis

• Interpretation of Coefficients Dummy Variables
  Design of Research Study

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Ballentine Diagrams
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How Does OLS Work?

• OLS chooses a,bx,by to minimize the sum of the
  squared residuals

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The OLS Estimated Coefficients
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Why Use OLS?

• Low cost to compute
• Small residuals/Highest R2
• Unbiasedness
• Efficient/small variance
• Consistency

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How Much of Y is Explained? R2 and Adjusted R2

• R Squared is the ratio of the explained sum of
  squares to the total sum of squares. It is the
  percentage of the variation of Y around its mean
  that can be explained by the regression equation.
• R Squared ESS/TSS

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Components of TSS
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LA Apartment Rents

• Review the Literature
• Specify the model
• Hypotheisze the expected signs of the
  coefficients
• Collect the data
• Estimate and evaluate the equation
• Document the results

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What Determines Rent?

• What kind of data will you need?
• Time series vs cross sectional data
• Aggregate data vs individual apartments
• What are likely sources of data?
• American housing survey
• Real estate ads

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Example Continued

• What will be the dependent variable?
• Monthly rent
• Monthly rent per room
• Monthly cost (include utilities, parking etc.)
• What explanatory variables should be included?
• Square footage
• Amenities

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Dummy Variables

• Dummy Variables take on value of zero or one.
• Intercept Dummy
• Slope Dummy

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LA Apartment Rents

• Dependent Variable
• Monthly rental price in nominal dollars
• Explanatory Variables
• SQFT, Total finished area of apartment in sq. ft.
• BD, Total number of bedrooms
• BA, Total number of bathrooms

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Apartment Rents, continued

• Dummy variables
• Variable takes on value of 0 or 1 depending on
  whether some condition holds.
• Dummy variables in data set
• FURN, furnished ALARM, built-in security alarm
  AC, air conditioning DISHW, dishwasher PARK,
  indoor parking POOL, pool GYM, gymTERR,
  terrace, PET, pets allowed FIREP, fireplace
  BEACH, beachfront property.

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Apartment Rents -- First Results
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Interpret the Results

• 100 additional square foot of space increases
  monthly rent by _______?
• What is the difference in rent between
  apartments, otherwise identical,but one has a
  terrace and the other doesnt? ________
• How much of variation in monthly rent
  explained?__________