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Ordinary least squares for a simple regression
P=20-2Q
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Suppose we have 4 observations
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on price and quantity:
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Obs. #QuantityPriceee*e
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1311-39
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261139
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356-416
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4104416
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Average6850
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A. Least squares principle: Find slope
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and intercept to minimize sum
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of squared residuals. Why?
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B. Residual =
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C. Residual Sum of Squares (RSS)=
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D. Using calculus and solving, we get
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These numbers give the OLS or least squares estimates
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of the true slopes.
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E. Now, calculate
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for each of the four observations.
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F. Now, calculate the residuals for the four observations.
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G. Add the residuals up. What do you get?
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17.65384615
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H. Calculate the standard error of the regression: SER=
8.826923077
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2.971013813
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I. Now calculate the Total Sum of Squares: TSS=
38ESS
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TSS
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J. Now calculate the Explained Sum of Squares: ESS=
20.34615385
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K.    Now calculate R2:
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since ESS+RSS=TSS. What does it mean?
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0.53542510121-0.4645748988
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L.     Now calculate
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. What does it mean?
0.303145
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-0.39371
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