1 / 10

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),

bruce-ellis
Download Presentation

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related