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Related Concept Videos

Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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Confidence Intervals01:21

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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On the Relationship Between Confidence Sets and Exchangeable Weights in Multiple Linear Regression.

Jolynn Pek1, R Philip Chalmers1, Georges Monette1

  • 1a York University.

Multivariate Behavioral Research
|October 19, 2016
PubMed
Summary

Understanding uncertainty in statistical models is key for strong conclusions. This study clarifies confidence sets (CSs) and exchangeable weights (EWs) in multiple linear regression, offering a framework and R code for their estimation.

Keywords:
Parameter uncertaintyconfidence setsexchangeable weightsmultiple linear regression

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Area of Science:

  • Statistical modeling
  • Psychometrics
  • Quantitative psychology

Background:

  • Statistical models describe empirical relationships, but conclusions depend on quantifying parameter uncertainty.
  • Multiple linear regression (MLR) involves two types of uncertainty: confidence sets (CSs) for estimation and exchangeable weights (EWs) for interpretation.

Purpose of the Study:

  • To clarify the relationship between CSs and EWs in MLR.
  • To introduce a general framework for estimating CSs and EWs.
  • To provide analytical relationships between CSs and EWs.

Main Methods:

  • Developed a general framework for estimating CSs and EWs using likelihood-based and Wald-type approaches.
  • Established analytical relationships between CSs and EWs.
  • Utilized empirical examples from studies on posttraumatic growth and graduate GPA.

Main Results:

  • Demonstrated the utility of CSs and EWs for drawing robust scientific conclusions.
  • Provided R code for estimating Wald-type CSs and EWs for regression weights.

Conclusions:

  • Considering both CSs and EWs is crucial for the scientific process.
  • The proposed framework and methods enhance the interpretation of regression weights in MLR.