Correlation Coefficient and ANOVA Table

Correlation Coefficient and ANOVA Table

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Correlation Coefficient

? Correlation Coefficient:

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Example: Correlation Coefficient

? Scenario:

? Question: ? Answer:

? Question: ? Answer:

Example: Correlation Coefficient

? Scenario:

? Question: ? Answer:

? Takeaway:

Properties of the Correlation Coefficient

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Note: Proofs of properties 1 and 2 require some knowledge of probability theory, covariance, and expectation.

Example: Correlation Same Sign as Slope

? Task:

? Answer:

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 as a Measure of Association

Population Correlation Coefficient

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Population

Correlation

Coefficient:

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Five different methods of doing inference with the correlation covered next class.

Univariate Normal Distribution

? Univariate Normal Distribution:

Bivariate Normal Distribution

? Bivariate Normal Distribution:

Conditional Distribution of at

? Conditional Distribution of and :

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Why is the bivariate normal distribution important?

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? coefficient of determination

Sums of Squares

? Total Sum of Squares:

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? Sum of Squares Due to Error:

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Coefficient of Determination

? Coefficient of Determination:

Example: Calculating

? Scenario:

? Question: ? Answer:

? Question: ? Answer:

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