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. |
Contents
Some Basic Results in Probability and Statistics | 1 |
Inferences in Regression Analysis | 3 |
Linear Regression with One Independent Variable | 21 |
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5-color analysis of variance ANOVA ANOVA table b₁ B₂ blocking variable Bonferroni C₁ Company example completely randomized design conclude C₂ confidence interval decision rule degrees of freedom denoted equal error sum error terms experimental units F test factor effects factor level means family confidence coefficient Figure fitted follows Hence independent variables indicator variables interactions interval estimate latin square level of significance linear regression matrix mean response mean sales mean squares normally distributed Note observations obtain parameters prediction prediction interval probability distribution procedure random variables Refer to Problem regression analysis regression coefficients regression function regression line response function sample sizes Source of Variation ẞ₁ SSAB SSE(F ẞo SSR(X₁ SSTO SSTR sum of squares test statistic transformation treatment effects Type I error variance model Variation SS df X₁ X₂ Y₁ Y₂ zero Σ Χ σ²