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Final Exam 1999 - of the error terms what do we know about...

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Statistics for Food and Resource Economics Final 1999 Attached is a table of corn yields and nitrogen, phosphorous and potash applied for acres of production in Illinois. 1. Compute the ordinary least squares estimates for the linear production function of corn as a function of each nutrient: i i i i K P N y 3 2 1 0 α α α α + + + = where y i is the corn yield in bushels per acre, N i is the nitrogen applied in pounds per acre, P i is the phosphorous applied in pounds per acre, and K i is the potash applied in pounds per acre. 2. Compute the variance matrix for each parameter assuming small sample properties. What assumptions are necessary to compute test statistics for the regression coefficients? What is the appropriate test for α 2 =0? 3. What is the relationship between ordinary least squares and maximum likelihood in linear models? How are the appropriate test statistics for maximum likelihood derived (in theory you don’t have to do them)? Are these statistics appropriate in small sample? 4. In the absence of specific distributional assumptions (such as normality
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Unformatted text preview: of the error terms) what do we know about the efficiency of ordinary least squares? Nitrogen (lbs./acre) Phosphorous (lbs./acre) Potash (lbs./acre) Corn (bu./acre) 127.00 60.00 90.00 140.00 202.00 104.00 120.00 110.00 88.00 24.00 90.00 61.00 150.00 69.00 120.00 138.00 200.00 0.00 0.00 150.00 153.30 52.60 126.60 102.00 139.00 35.00 90.00 160.00 150.00 60.00 120.00 115.00 160.00 40.00 50.00 165.00 180.00 37.00 120.00 140.00 160.00 30.00 60.00 135.00 182.70 76.80 127.70 160.00 154.00 60.00 80.00 151.10 196.00 92.00 90.00 143.10 172.30 57.50 120.00 154.18 227.08 69.00 60.00 155.00 147.00 69.00 150.00 45.70 165.84 72.00 160.00 115.00 104.50 57.50 21.00 115.00 71.80 69.00 90.00 105.00 101.64 0.00 0.00 100.00 203.00 46.00 150.00 129.00 125.40 69.00 90.00 160.00 180.00 0.00 0.00 115.00 175.00 80.00 80.00 120.00 167.40 50.60 48.00 167.90 214.00 138.00 180.00 150.00 200.00 0.00 200.00 165.00 195.00 104.00 135.00 149.00 199.00 0.00 0.00 143.00...
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