## 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 4

Joint, Marginal, and Conditional Probability Distributions Let the joint probability

function for the two random variables y and Z be

(Y = Y„Z = Zt) s = 1,...,*; t = l,...,m The marginal probability function of V,

Joint, Marginal, and Conditional Probability Distributions Let the joint probability

function for the two random variables y and Z be

**denoted**g(Y, Z): (1.16) g(Y„Zt)=P(Y = Y„Z = Zt) s = 1,...,*; t = l,...,m The marginal probability function of V,

**denoted**...Page 409

Thus, to estimate p?.234, we need the total sum of squares for yj,

Yt). Then we require the regression sum of squares when K, is regressed on Y2 ,

X3 , and Y4 ,

Thus, to estimate p?.234, we need the total sum of squares for yj,

**denoted**SSTO(Yt). Then we require the regression sum of squares when K, is regressed on Y2 ,

X3 , and Y4 ,

**denoted**SSR( Y2, Y3, Y4). The estimator,**denoted**/??.234, ...Page 772

24.2 MODEL A latin square design involves the effect of the row blocking variable

,

the treatment effect,

...

24.2 MODEL A latin square design involves the effect of the row blocking variable

,

**denoted**by p; , the effect of the column blocking variable,**denoted**by Kj , andthe treatment effect,

**denoted**by xk. It is necessary to assume that no interactions...

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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