Correlation Coefficient and ANOVA Table

[Pages:8]Correlation Coefficient and ANOVA Table

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Correlation Coefficient

? Correlation Coefficient:

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Example: Correlation Coefficient

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? Question: ? Answer:

? Question: ? Answer:

Example: Correlation Coefficient

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? 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

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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

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? Question: ? Answer:

? Question: ? Answer:

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Example: Calculating

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? Question: ? Answer: ? Takeaway:

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Example: Perfect Linear Relationship

? Question:

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Example: No Linear Relationship

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ANOVA Table for Straight Line Regression

? Analysis of Variance (ANOVA) Table:

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Types of Variation

? Explained Variation:

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? Unexplained Variation:

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ANOVA Table for Simple Linear Regression

Fundamental Equation of Regression Analysis

F-Distribution and ANOVA Table Test Statistic

? F-Distribution:

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? Test Statistic:

Example: Using the ANOVA Table

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? Task:

? Hypotheses: ? Test Statistic: ? Critical Values: P-Value:

? Conclusion:

Example: Comparing ANOVA Table and Test for Slope

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? Question:

? Answer:

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