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In this final topic, we consider using the estimated regression line to estimate the mean response at a given value of the explanatory (x) variable. The standard error…
Estimation and Prediction for a Specific Value of…
From Jane Harvill
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In this lesson, the assumption of the normality of errors, and hence the normality of the responses is added to the simple linear regression model. The consequences are…
Estimation and Testing with Normal Errors
From Jane Harvill
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In this lesson, two models for paired data are introduced that are also called simple linear regression models. In the previous lesson, the estimators we derived…
Models and Distributions
From Jane Harvill
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Methods for estimating the coefficients in the simple linear regression model are investigated. The least squares method is a purely mathematical approach, requiring no…
Estimation of Model Parameters
From Jane Harvill
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In analysis of variance, we looked at how one factor (a discrete or a categorical variable) influenced the means of a response variable. We now turn to simple linear…
Introduction to Simple Linear Regression
From Jane Harvill
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Linear combinations of means, and in particular contrasts, play an important role in analysis of variance (ANOVA). Through understanding and analyzing contrasts,…
Linear Combinations of Means
From Jane Harvill
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In this lesson, we consider the "Classic ANOVA Hypothesis." Assumptions on the cell means model are described and used to devise an F test for the hypothesis.
The Classic ANOVA Hypothesis
From Jane Harvill
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Up until now, we have modeled random variables with a probability mass function or a probability density function. We then discussed in detail the theory behind…
Introduction to Oneway Analysis of Variance…
From Jane Harvill
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In this lesson, some approximate and asymptotic versions of confidence sets are explored. The purpose here is to illustrate some methods that will be of use in more…
Asymptotic Evaluations for Interval Estimation
From Jane Harvill
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Asymptotic Evaluations for Hypothesis Testing 10 of 15
Asymptotic Evaluations for Hypothesis Testing
The lesson describes a few methods for deriving some tests in complicated problems in which no optimal test (such as the uniformly most powerful test) exists or is…Asymptotic Evaluations for Hypothesis Testing
From Jane Harvill
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There are several properties to be considered when considering a point estimator from an asymptotic perspective. In this lesson, the concepts of consistency and…
Asymptotic Evaluations of Point Estimators
From Jane Harvill
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Loss function for confidence sets (or credible sets) combines the maximum coverage probability and shortest interval criteria into one function - the loss function. The…
Loss Function Optimality for Interval Estimation
From Jane Harvill
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The goal of obtaining a smallest confidence set with a specified coverage probability can also be attained using Bayesian criteria. If we have a posterior distribution…
Bayesian Credible Set Optimality
From Jane Harvill
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Since there is a one-to-one correspondence between confidence sets and tests of hypotheses, there is some correspondence between the optimality of tests and the…
Test-Related Optimality
From Jane Harvill
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There are a number of methods for finding an interval estimator. In the frequentist domain, the three methods previously discussed are inverting the acceptance region…
Size and Coverage Probability
From Jane Harvill
442 plays 0
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