## 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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Results 1-3 of 67

Page 313

FIGURE 9.6

Lot Size We consider now how indicator variables may be used to fit piecewise

linear regressions consisting of two pieces. We take up the case where Xp, the

point where the slope changes, is known. We return to our lot size

which it is known that the slope changes at Xp = 500. The model for our

+ e, where ...

FIGURE 9.6

**Illustration**of Piecewise Linear Regression Unit Cost y\ 0 Xp = 500 XLot Size We consider now how indicator variables may be used to fit piecewise

linear regressions consisting of two pieces. We take up the case where Xp, the

point where the slope changes, is known. We return to our lot size

**illustration**, forwhich it is known that the slope changes at Xp = 500. The model for our

**illustration**may be expressed as follows: (9.18) Yi = p0 + pxXn + P2(Xn - 500)A-i2+ e, where ...

Page 322

FIGURE 9.9

Binary Probability That Firm Has Industrial Relations Department E(Y) I - Size of

Firm response function for a dependent indicator variable. Here, the indicator

variable Y refers to whether or not a firm has an industrial relations department,

and the independent variable X is size of firm. The response function in Figure

9.9 shows the probability that firms of given size have an industrial relations

department.

FIGURE 9.9

**Illustration**of Response Function when Dependent Variable IsBinary Probability That Firm Has Industrial Relations Department E(Y) I - Size of

Firm response function for a dependent indicator variable. Here, the indicator

variable Y refers to whether or not a firm has an industrial relations department,

and the independent variable X is size of firm. The response function in Figure

9.9 shows the probability that firms of given size have an industrial relations

department.

Page 464

For example, package designs 2 and 4 in our

whereas 1 and 3 did. The analyst might therefore also wish to study: (I) whether

or not the use of cartoons affects mean sales, (2) whether the two designs with

cartoons differ in sales effectiveness, and (3) whether the two designs without

cartoons differ in sales effectiveness. The decomposition of SSTR for these

questions would follow the same principles of group decomposition just

explained. However ...

For example, package designs 2 and 4 in our

**illustration**did not utilize cartoons,whereas 1 and 3 did. The analyst might therefore also wish to study: (I) whether

or not the use of cartoons affects mean sales, (2) whether the two designs with

cartoons differ in sales effectiveness, and (3) whether the two designs without

cartoons differ in sales effectiveness. The decomposition of SSTR for these

questions would follow the same principles of group decomposition just

explained. However ...

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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 | |

23 other sections not shown

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### Common terms and phrases

95 percent analysis of variance ANOVA ANOVA Table appropriate block design 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 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 standard deviation sum of squares test statistic three-factor transformation treatment effects treatment means two-factor study Type I error variance model Westwood Company zero