Team B: Simple Linear Regression

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Team B Simple Linear Regression

• Ian Charles
• Lisa Clover
• Charles Thompson
• Maura Thill
• John Archibald

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Main Menu

• Definition of Linear Regression
• Case Description
• Analysis
• Scat-O-Gram
• Correlation
• Coefficient of Determination
• Adjusted r2
• Etc...
• Resolution

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Case Description

• Simple Linear Regression Analysis
• The means of using one variable to predict
  another variable
• The analysis of the cost of Marin County homes
  and their corresponding square footage
• Independent VariableSquare Footage
• Dependent VariableCost

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Questions to Answer

• Is there a relationship between the price of
  homes in Marin and the square footage?
• Does the square footage determine the cost?
• How sure are we?

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Data

• Independent Y
• Price
• 84,000-6,998,000
• Mean849,538
• Median559,000
• Mode449,000
• Count 180

• Dependent X
• Square Footage
• Range 677-18,000
• Mean2,689
• Median2,400
• Mode3,000
• Count180

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Scat-O-Gram
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Correlation

• 81.9
• Reflects a strong association between the square
  footage of a home and its cost

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Coefficient of Determination

• 67.0
• Illustrates that 67.0 of the variation in price
  can be explained by the Square Footage of the home

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Adjusted r2

• 66.9
• Although some researchers suggest adjusting the
  r2 to the sample size, it varies little from the
  original r2

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Regression Sum of Squares

• SSRThe difference between (Ybar-Y)
• The residual which can be explained
• 1.28E14

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Error Sum of Squares

• SSE(Y-Y)
• Represents that part of the variation in Y that
  cannot be explained by the regression
• 6.27E13

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Total Sum Squares

• A measure of variation of Y values around Ybar
• SSTSSRSSE
• 1.91E14

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F Test

• FMSR/MSE
• 362.951.28E14/3.52E11

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Reject the Ho

• 362.9559gt3.84 (120 degrees of freedom)

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Significance of F

• 7.9E-45lt.05
• Yes, there is a significant relationship

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The Linear Relationship

• YiBoB1Xiei
• Yi-471279491.17Xiei
• Yi-471279491.17(2500)
• Yi-4712791227925756,646

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Four Assumptions of Regression Correlation

• Normality
• Homoscedasticity
• Independence of Errors
• Linearity

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Residual Analysis
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T Stat

• tb1/Sb1
• t491.17/25.7819.05
• 19.05gt1.9799
• Ho We reject the null hypothesis

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95 Confidence Interval

• b1tn-2Sb1
• 491.17(1.979925.78)
• 542,052
• 491.17-(1.979925.78)
• 440,298

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Conclusion

• Yes, there is a relationship between home prices
  and square footage.
• Price IS determined by square footage.
• There is less than a 1 chance that there is no
  relationship.