## 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 26

In the population of observations associated with the sampled process, there is a

In the population of observations associated with the sampled process, there is a

**probability distribution**of Y for each level of X. 2. The means of these**probability****distributions**vary in some systematic fashion with X. Example. Consider again ...Page 399

Such conditional inferences require the use of conditional

The conditional density function of yt, for any given value of Y2 , is denoted /(Yt |

Y2), and is ...

Such conditional inferences require the use of conditional

**probability****distributions**, which we discuss next. Conditional**Probability Distributions**of y,The conditional density function of yt, for any given value of Y2 , is denoted /(Yt |

Y2), and is ...

Page 400

I. The conditional

Imagine that we slice a bivariate normal distribution vertically at a given value of

Y2, say at Yh2. That is, we slice it parallel to the V, axis. This slicing is shown in ...

I. The conditional

**probability distribution**of V,, for any given value of V2,is normal.Imagine that we slice a bivariate normal distribution vertically at a given value of

Y2, say at Yh2. That is, we slice it parallel to the V, axis. This slicing is shown in ...

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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