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Solutions for Chapter 12.7: Estimation and Prediction Using the Fitted Line

Introduction to Probability and Statistics 1 | 14th Edition | ISBN: 9781133103752 | Authors: William Mendenhall Robert J. Beaver, Barbara M. Beaver

Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752

Introduction to Probability and Statistics 1 | 14th Edition | ISBN: 9781133103752 | Authors: William Mendenhall Robert J. Beaver, Barbara M. Beaver

Solutions for Chapter 12.7: Estimation and Prediction Using the Fitted Line

Since 8 problems in chapter 12.7: Estimation and Prediction Using the Fitted Line have been answered, more than 9268 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. Chapter 12.7: Estimation and Prediction Using the Fitted Line includes 8 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
  • Adjusted R 2

    A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

  • Analytic study

    A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

  • Attribute

    A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

  • Bayes’ estimator

    An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

  • Bernoulli trials

    Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

  • Biased estimator

    Unbiased estimator.

  • Block

    In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

  • C chart

    An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

  • Central limit theorem

    The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

  • Consistent estimator

    An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

  • Correction factor

    A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

  • Crossed factors

    Another name for factors that are arranged in a factorial experiment.

  • Curvilinear regression

    An expression sometimes used for nonlinear regression models or polynomial regression models.

  • Deming

    W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

  • Discrete distribution

    A probability distribution for a discrete random variable

  • Event

    A subset of a sample space.

  • Exponential random variable

    A series of tests in which changes are made to the system under study

  • Fixed factor (or fixed effect).

    In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

  • Frequency distribution

    An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

  • Hat matrix.

    In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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