Question: The true model is Y * i = β 1 + βX * i + u i ¦¦¦¦¦¦¦¦¦¦¦.. (1) But because of errors of measurement

The true model is

Y*i = β1 + βX*i + ui €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.. (1)

But because of errors of measurement you estimate

Yi = α1 + α2Xi + vi €¦€¦€¦€¦€¦€¦€¦€¦. (2)

where Yi = Yˆ—i+ εi and Xi = Xˆ—i + wi , where εi and wi are measurement errors.

Using the data given in the following table, document the consequences of estimating model (2) instead of the true model (1).

y* х* х 80.0940 -7.8655 75.4666 80.00 67.6011 0.0940 2.4666 74.9801 102.8242 75.4438 91.5721 -8.4279 100.00 0.4636 -10

y* * 80.0940 -7.8655 75.4666 80.00 67.6011 0.0940 2.4666 74.9801 102.8242 75.4438 91.5721 -8.4279 100.00 0.4636 -10.0199 120.00 109.6956 112.1406 6.8714 2.1406 5.5969 5.8242 125.7651 140.00 129.4159 145.5969 3.6509 16.7651 -14.4965 106.5035 160.00 104.2388 168.5579 -2.2647 8.5579 131.4318 149.3693 180.00 125.8319 171.4793 -5.5999 -8.5207 -1.5682 200.00 203.5366 153.9926 4.6233 3.5366 4.3693 143.8628 177.5218 220.00 152.9208 222.8533 9.0579 2.8533 -13.1372 240.00 176.3344 232.9879 -1.1874 -7.0120 8.5218 182.2748 174.5252 -7.7496 260.00 261.1813 1.1813 1.2748

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