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# AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH - PowerPoint PPT Presentation

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 4302ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

Chapter 14:

F Tests

• 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)

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

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

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

• 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

• 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

Ŷi = 474.05 + 1.46X1 +26.32X2

Test:

H0: β1 = β2 =0

Ha: β1 and/or β2≠ 0