## 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 11

... 22.73 so that the decision rule is: If F ^ 22.73, conclude Ct If F > 22.73,

Confidence Intervals. There is a direct relation between tests and confidence

intervals.

... 22.73 so that the decision rule is: If F ^ 22.73, conclude Ct If F > 22.73,

**conclude C2**Since F = 24 > 22.73, we**conclude C2**. Relation between Tests andConfidence Intervals. There is a direct relation between tests and confidence

intervals.

Page 13

Choose among the alternatives: C, : = C2 : /i, # ih when a is to be controlled at .10

and the data are those of Example 3. ... A, conclude C, C2: /t, > it2 If F- 2 > A,

...

Choose among the alternatives: C, : = C2 : /i, # ih when a is to be controlled at .10

and the data are those of Example 3. ... A, conclude C, C2: /t, > it2 If F- 2 > A,

**conclude C2**where : A ^ t(\ - a; nt +n2 - 2)s(? - 2) We require: f(.95; 28) = 1.701 Ai...

Page 17

TABLE 1.4 Decision Rules for Tests concerning Variances a\ and a\ of Two

Normal Populations Alternatives Decision Rule (a) _2 C,:af = CTi IfF(a/2;n,- l,n2-

1)<4 Sz < F(l - a/2; n, - I, n2 - 1), conclude C, C2: a\ 7^ at Otherwise

b) Ct: ...

TABLE 1.4 Decision Rules for Tests concerning Variances a\ and a\ of Two

Normal Populations Alternatives Decision Rule (a) _2 C,:af = CTi IfF(a/2;n,- l,n2-

1)<4 Sz < F(l - a/2; n, - I, n2 - 1), conclude C, C2: a\ 7^ at Otherwise

**conclude C2**(b) Ct: ...

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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