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In Multiple Regression with K Independent Variables, the T-Tests of the Individual

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In multiple regression with k independent variables, the t-tests of the individual coefficients allow us to determine whether βi0\beta _ { i } \neq 0 (for i = 1, 2, …, k), which tells us whether a linear relationship exists between xix _ { i } and y.

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Definitions:

Significance Level

The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true, serving as a threshold for determining the statistical significance of an effect.

Degrees of Freedom

The number of values in the final calculation of a statistic that are free to vary.

Dependent Means

Refers to the average outcomes within groups that are related or paired, often used in the analysis of experiments or studies.

Individuals

Refers to distinct objects or entities being studied or observed in research or statistical analysis, often representing people, animals, or units in an experiment or survey.

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