Solutions for Chapter 11.3: The Coefficients of Determination

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition | ISBN: 9781119285427 | Authors: Kishor S. Trivedi

Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

ISBN: 9781119285427

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition | ISBN: 9781119285427 | Authors: Kishor S. Trivedi

Solutions for Chapter 11.3: The Coefficients of Determination

Solutions for Chapter 11.3
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This expansive textbook survival guide covers the following chapters and their solutions. Since 2 problems in chapter 11.3: The Coefficients of Determination have been answered, more than 1122 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Chapter 11.3: The Coefficients of Determination includes 2 full step-by-step solutions. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427.

Key Statistics Terms and definitions covered in this textbook
  • Acceptance region

    In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

  • Alternative hypothesis

    In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

  • Analysis of variance (ANOVA)

    A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

  • Bernoulli trials

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

  • 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.

  • Comparative experiment

    An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

  • Completely randomized design (or experiment)

    A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

  • Consistent estimator

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

  • Correlation matrix

    A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

  • Critical region

    In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

  • Decision interval

    A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

  • Defect

    Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

  • Degrees of freedom.

    The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

  • Deining relation

    A subset of effects in a fractional factorial design that deine the aliases in the design.

  • Design matrix

    A matrix that provides the tests that are to be conducted in an experiment.

  • Erlang random variable

    A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

  • Estimator (or point estimator)

    A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

  • Experiment

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

  • Gamma function

    A function used in the probability density function of a gamma random variable that can be considered to extend factorials

  • Harmonic mean

    The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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