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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH. Chapter 14: F Tests. F Test. State the hypotheses Determine the value of F* Choose the level of significance ( α ) Use tables to determine F c Apply decision rule r df of the numerator (number of restrictions),

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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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  1. AAEC 4302ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 14: F Tests

  2. F Test • State the hypotheses • Determine the value of F* • Choose the level of significance (α) • Use tables to determine Fc • Apply decision rule r df of the numerator (number of restrictions), n-k-1 df of the denominator (k –number of regressors in the unrestricted model)

  3. Most Common Applications of F Test • Some of the coefficients are equal to zero: H0: β2 = β3 =0 H1: β2 and/or β3≠ 0 Models 1 and 3 in the table 14.1 • All coefficients are equal to zero: H0: β1 = β2 = . . . =βk= 0 H1: βj≠ 0 for at least one j, j = 1, . . .,k

  4. Most Common Applications of F Test • F test for a set of dummy variables to be equal to zero: Table 14.1 model 5 H0: β5 = β6 = β7 = 0 H1: β5≠ 0 and/or β6≠ 0 and/or β7≠ 0 • A single regression coefficient is equal to zero: H0: βj = 0 H1: βj≠ 0

  5. Most Common Applications of F Test • Testing a hypothesis that specifies a relation among coefficients: H0: β1 = β2 H1: β1≠ β2 CONi = β0 + β1 LABINCi + β2 PROPINCi + ui CONi = β0 + β1 TOTINCi + ui , r=1

  6. The Chow Test • Test for equality of coefficients Model 3 in table 14.1 The unrestricted form, allowing for differences, consists of two estimated regressions 3 one for blacks and one for whites SSRu = 0.6713+16.9793=17.6506 Restricted form is regression 3 in table 14.1

  7. The Chow Test • In time-series data Chow test is the test for structural stability H0: coefficients are the same in both periods H1: Coefficients are different in both periods LNMi = β0 + β1LNGNPi + ui Two time periods: 1956-1970 and 1971-1980 H0: β01 = β02 and β11 = β12 H1: β01≠ β02 and β11≠β12

  8. F-Test Example Ŷi = 474.05 + 1.46X1 +26.32X2 Test: H0: β1 = β2 =0 Ha: β1 and/or β2≠ 0

  9. F-Test Example RSS = 1687891.751 SSE = 4086450.184

  10. F-Test Example F* = 27.06 Fcr2,131 at α=0.01≈ 4.78 Since the calculated F* is greater than the Fcr => you are 99% sure that both X1 and X2 have statistical impact on Y.

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