Significance of regression

Correlation is not significant because of difference in sign between a and 0. Significance of r is <90% CL unless otherwise noted. Confidence levels for significance of regression are reported as superscripts on F values. Confidence levels for significance of and h are reported as superscripts on values of Sq, s, and S),. 

In Sections 11.3 and 11.4 the value increased from 0.479 to 0.794 and the F-ratio for the significance of regression increased from the 97.3% to the 99.6% level of confidence when the term was added to the model. Is it possible that in some instances will increase, but the significance of regression will decrease If so, why [See, for example, Neter, Wasserman, and Kutner (1990), p. 229.]... 

A system is thought to be described between Xj = 0 and xt = 10 by the model Fi, = + /J,xu + rv. What is the minimum number of experiments that will allow the model to be fit, the significance of regression to be tested, and the lack of fit to be tested How should these experiments be distributed along xf. Why ... 

When estimating the significance of regression coefficients, these equations are used ... 

A check of statistical significance of regression coefficients for reproducibility var-... 

Other regression coefficients are determined in accord with formulas for orthogonal designing. A check of significance of regression coefficients is given in Sect. 2.4.1, and the check of lack of fit of regression model is in Sect. 2.4.3. 

A check of statistical significance of regression coefficients (Sect. 2.4.2), indicates that regression coefficients bn and b22 are statistically insignificant. The final form of the second-order regression model with 95% confidence may be given in the form ... 

The obtained regression model is adequate with 95% confidence. A check of significance of regression coefficients, in accord with Sect. 2.4.2, is completed thus ... 

A tabular value FT=1.85 is obtained for fAD=10 and fE=25(25-l)=600 from Table E. The regression model is with 95% confidence adequate because FRstatistical significance of regression coefficients, use formulas from Sect. 2.4.2. 

A check of significance of regression coefficients shows that with 95% confidence the following regression coefficients are statistically significant b0 hi b2 b3 b12 and b22. The second-order regression model has this form ... 

As said before, linear models are used to reach (move towards) optimum, so that the significance of regression coefficients is an assumption for successful application of the steepest ascent method. Linear models, therefore, include as many factors as possible, and full factorial experiments are even replicated with increased factor variation intervals. 

The linear model by application of FRFE 24-1 was obtained in Problem 2.19. After checking the significance of regression coefficients, this linear model has been obtained ... 

To evaluate the fit of the calculated model, usually ANOVA is applied (1, 7,17,116). ANOVA will evaluate the data set variation. Often a test for the significance of regression and a lack-of-fit test are performed (7,17,116). A model is then considered adequate and well fitted to the data when both a significant regression and a nonsignificant lack-of-fit occur. 

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