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Correlation Analysis - PowerPoint PPT Presentation

Correlation Analysis. X and Y are random variables that are jointly normally distributed and, in addition, that the obtained data consists of a random sample of n independent pairs of observations (X 1 , Y 1 ), (X 2 , Y 2 ), . . . . (X n , Y n ) from an underlying bi-variate normal population.

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PowerPoint Slideshow about ' Correlation Analysis' - kato-blanchard

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Presentation Transcript

X and Y are random variables that are jointly normally distributed and, in addition, that the obtained data consists of a random sample of n independent pairs of observations (X1, Y1), (X2, Y2), . . . . (Xn, Yn) from an underlying bi-variate normal population.

Y = f(X)

any relationships?

Relationships – 3 goals if any, how strong?

nature or form

Two of the most powerful and versatile approaches for investigating variable relationships are correlation analysis and regression analysis.

• Measures the strength of the relationship between two or more variables

• Correlation

• Measures the degree to which there is an association between two internally scaled variables

• Used to understand the nature of the relationship between two or more variables

• A dependent or response variable (Y) is related to one or more independent or predictor variables (Xs)

• Object is to build a regression model relating dependent variable to one or more independent variables

• Model can be used to describe, predict, and control variable of interest on the basis of independent variables

Yi = βo + β1 xi + εi

Where

• Y

• Dependent variable

• X

• Independent variable

• βo

• Model parameter

• Mean value of dependent variable (Y) when the independent variable (X) is zero

• β1

• Model parameter

• Slope that measures change in mean value of dependent variable associated with a one-unit increase in the independent variable

• εi

• Error term that describes the effects on Yi of all factors other than value of Xi

• Calculate point estimate bo and b1 of unknown parameter βo and β1

• Obtain random sample and use this information from sample to estimate βo and β1

• Obtain a line of best "fit" for sample data points - least squares line

Yi = bo + b1 xi

• A linear combination of predictor factors is used to predict the outcome or response factors

• Involves computation of a multiple linear regression equation

• More than one independent variable is included in a single linear regression model