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F Distributions

F Distributions. F distributions are similar to a Chi-Square Distributions, but have two parameters, df den and df num. The F Test for Model Utility. The regression sum of squares denoted by SSReg is defined by SSREG = SSTo - SSresid. The F Test for Model Utility.

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F Distributions

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  1. F Distributions F distributions are similar to a Chi-Square Distributions, but have two parameters, dfden and dfnum.

  2. The F Test for Model Utility The regression sum of squares denoted by SSReg is defined by SSREG = SSTo - SSresid

  3. The F Test for Model Utility

  4. The F Test Utility of the Model y = a + b1x1 + b2x2 + … + bkxk + e • Null hypothesis: • H0: b1 = b2 = … = bk =0 • (There is no useful linear relationship between y and any of the predictors.) • Alternate hypothesis: • Ha: At least one among b1, b2, … , bk is not zero • (There is a useful linear relationship between y and at least one of the predictors.)

  5. The F Test Utility of the Model y = a + b1x1 + b2x2 + … + bkxk + e

  6. The F Test Utility of the Model y = a + b1x1 + b2x2 + … + bkxk + e The test is upper-tailed, and the information in the Table of Values that capture specified upper-tail F curve areas is used to obtain a bound or bounds on the P-value using numerator df = k and denominator df=n-(k+1). Assumptions: For any particular combination of predictor variable values, the distribution of e, the random deviation, is normal with mean 0 and constant variance.

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