# Calc - Some Calculations to do the Regression example...

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1 Some Calculations to do the Regression example worked by the computer in the handout Row i x i y () 2 i x x ii x xy y −− 1 100 40 90000 6000 2 200 50 40000 2000 3 300 50 10000 1000 4 400 70 0 0 5 500 65 10000 500 6 600 65 40000 1000 7 700 80 90000 6000 2800 i x = 420 i y = 2 280, 000 i x x −= 16,500 xy = Now lets compute the slope coefficient using formula (14.6) on page 543. 1 2 1 1 16500 280,000 .0589286 i x b xx b b = = = Since the mean of X is 400, and the mean of Y is 60, formula (14.7) gives the intercept. 01 60 (.0589286) 400 36.4286 by b x =− = − = We can use the estimated regression line to generate predicted values, using the fact that ± .. Ybb X X i =+ = + 36 4286 0589286 Row ˆ yy ˆ 2 ˆ 2 2 ˆ 1 -2.3214 -20 -17.6786 5.389 400 312.532 2 1.7857 -10 -11.7857 3.189 100 138.903 3 -4.1071 -10 -5.8929 16.869 100 34.726 4 10.0000 10 0.0000 100.000 100 0.000 5 -0.8929 5 5.8929 0.797 25 34.726 6 -6.7857 5 11.7857 46.046 25 138.903 7 2.3214 20 17.6786 5.389 400 312.532 2 ˆ = 177.68 2 i = 1150.0 2 ˆ i = 972.32 By equation (14.12) on page 554, 2 2 2 ˆ i i r = , which in this case is r 2 972 32 1150 0 845496 == .

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2 To calculate the mean square error (our estimate of σ 2 ) we use formula (14.15) on page 561.
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Calc - Some Calculations to do the Regression example...

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