## Applied linear statistical models: regression, analysis of variance, and experimental designsSome basic results in probability and statistics. basic regression analysis. Linear regression with one independent variable. Inferences in regression analysis. Aptness of model and remedial measures. Topics in regression analysis - I. General regression and correlation analysis. Matrix appreach to simple regression analysis. Multiple regression. Polymonial regression. Indicator variables. Topics in regression analysis - II. Search for "best" set of independent variables. Normal correlation models. Basic analysis of variance. Single - factor analysis of variance. Analysis of factor effects. Implementation of ANOVA model. Topics in analysis of variance - I. Multifactor analysis of variance. Two factor analysis of variance. Analysis of two - factor studies. To pics in analysis of variance - II. Multifactor studies. Experimental designs. Completely randomized designs. Analysis of covariance for completely randomized designs. Randomized block designs. Latin square designs. |

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Page 80

or, using the notation in (3.41), (3.43), and (3.44): (3.47a)

prove this basic result in the analysis of variance, we proceed as follows: I(Yi-Y)2

= I[(?i-Y)+(Yi-?i)]2 = 2 [(?, - Y)2 + (Yi - f,Y + 2(?i - F)(y, - ?,)] = I (?t - y)2 + Z(yt- Yty ...

or, using the notation in (3.41), (3.43), and (3.44): (3.47a)

**SSTO**= SSR + SSE Toprove this basic result in the analysis of variance, we proceed as follows: I(Yi-Y)2

= I[(?i-Y)+(Yi-?i)]2 = 2 [(?, - Y)2 + (Yi - f,Y + 2(?i - F)(y, - ?,)] = I (?t - y)2 + Z(yt- Yty ...

Page 89

Thus,

considered. Similarly, SSE measures the variation in the 7, , or the uncertainty in

predicting y, when a regression model utilizing the independent variable

Misemployed.

Thus,

**SSTO**is a measure of the uncertainty in predicting Y when X is notconsidered. Similarly, SSE measures the variation in the 7, , or the uncertainty in

predicting y, when a regression model utilizing the independent variable

Misemployed.

Page 260

For this, the ANOVA identity is: (7.75)

Xt) by its equivalent in (7.70), we obtain: (7.75a)

SSE(Xt, X2) Replacing SSE(X,, X2) by its equivalent in (7.74), we obtain: (7.75b)

...

For this, the ANOVA identity is: (7.75)

**SSTO**= SSR(X,) + SSE(X,) Replacing SSE(Xt) by its equivalent in (7.70), we obtain: (7.75a)

**SSTO**= SSR{X,) + SSRiX^X,) +SSE(Xt, X2) Replacing SSE(X,, X2) by its equivalent in (7.74), we obtain: (7.75b)

...

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### Contents

Some Basic Results in Probability and Statistics | 1 |

Linear Regression with One Independent Variable | 21 |

Inferences in Regression Analysis | 53 |

Copyright | |

22 other sections not shown

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### Common terms and phrases

95 percent analysis of variance ANOVA appropriate blocking variable Bonferroni column Company example completely randomized design conclude C2 confidence interval correlation covariance analysis decision rule degrees of freedom denoted equal error sum error terms error variance experimental units factor effects factor level means family confidence coefficient Figure follows Hence illustration independent variables indicator variables interval estimate latin square latin square design level of significance linear regression main effects matrix mean response method normally distributed Note observations obtain parameters percent confidence prediction prediction interval probability distribution procedure random variables Refer to Problem regression analysis regression approach regression coefficients regression function regression line residual plots response function sample sizes shown significance of 05 Source of Variation SSAB SSE(F SSE(R SSTO SSTR sum of squares test statistic three-factor transformation treatment effects treatment means two-factor study Type I error variance model vector Westwood Company zero