hw8ans - Statistics 500 Fall 2009 Solutions to Homework 8...

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Statistics 500 – Fall 2009 Solutions to Homework 8 1 1. Linerboard and regression tests My fitted model was: ) log( 34 . ) log( 286 . ) log( 543 . ) log( 126 . 762 . 1 ) log( labor deprec energy rawmat product + + + + = () ( ) ( ) ( ) 34 . 0 286 . 0 543 . 0 126 . 0 ) 762 . 1 exp( labor deprec energy rawmat product = Variable DF Estimate Std Error t Value Pr > |t| Intercept 1 -1.76206 0.79507 -2.22 0.0384 lograwmat 1 0.12634 0.04316 2.93 0.0083 logenergy 1 0.54267 0.07886 6.88 <.0001 logdeprec 1 0.28626 0.06516 4.39 0.0003 loglabor 1 0.33994 0.14459 2.35 0.0291 (a) This is the F-test of the entire regression model: Sum of Mean Source DF Squares Square F Value Pr > F Model 4 4.83013 1.20753 647.29 <.0001 Error 20 0.03731 0.00187 Corrected Total 24 4.86744 The test statistic is F=647, with p < 0.0001. There is very strong evidence that at least one regression slope differs from zero. * Again, remember the overall test does not tell you that all slopes are non-zero, just at least one. (b) Test 1 : 4 3 2 1 0 = + + + β H You can test this hypothesis three ways. Each gives you the same p-value and conclusion, but the test statistics may not be the same. P < 0.017. There is evidence that the sum of the coefficients is not 1. In econometric terms, there is not constant return to scale. 1) Estimate 4 3 2 1 + + + and its standard error, then construct a t-test: T = (estimate of sum - 1)/se = (1.295-1)/0.114 = 2.59. You can get the estimate and s.e. from proc glm; … estimate rawmat 1 energy 1 deprec 1 labor 1; Parameter Estimate Error t Value Pr > |t| sum1 1.29521599 0.11377588 11.38 <.0001 * The t-test provided by SAS tests the wrong hypothesis (sum = 0). 2) Use a test statement in proc reg to construct the F statistic for a linear constraint. Source DF Mean Sq F Value Pr > F Numerator 1 0.01256 6.73 0.0173 Denominator 20 0.00187 3) Construct a reduced model corresponding to the null hypothesis.
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Statistics 500 – Fall 2009 Solutions to Homework 8 2 Full model: Model in (a) Reduced model: ( ) ε β + + + + + = 4 3 2 1 3 3 2 2 1 1 0 log 1 log log log ) log( X X X X Y Or: [] [ ][ ] + + + + = 4 3 3 4 2 2 4 1 1 0 4 log log log log log log ) log( ) log( X X X X X X X Y (c) You need the s.e. of the sum, which you can get from the estimate (above) command or by
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hw8ans - Statistics 500 Fall 2009 Solutions to Homework 8...

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