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Social Statistic

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Submitted By CherieLing
Words 406
Pages 2
SOWK 2502
Simple Regression Analysis
Example

Refer to the example given in the example from the previous lecture on correlations. Having established that there is a strong correlation between weeks in an assertiveness training program and scores on the Assertiveness Scale, Sheila is now interested in being able to predict scores on assertiveness based on number of weeks in the program. Using the same data set, she was able to create an equation which would allow her to make this prediction. This equation is called the Least-Squares Regression Equation.

Client weeks score

Mary 1 30 June 2 30 Lynn 3 40 Shelly 3 50 Liz 4 60 Carol 5 60 Debbie 5 60 Anne 7 90 Sue 8 80 Helen 8 90

X Y X² Y² XY 46 590 266 39300 3190

Least Squares Regression Equation

Y1 = a + b(X)

Y1 = predicted Y value from a particular X value a = The point where the regression line would intersect the Y axis, b = The slope of the line, where the amount of change in Y is directly related to amount of change in x. x = A selected value of the predictor variable used to predict the value of the outcome variable

Slope Formula: b = N XY - (X)( Y) N X2 - (X)2

Where: b = Slope N = Number of cases XY = Sum of xy column X2 = Sum of x2 column Y2 = Sum of y2 column X = Sum of x column Y = Sum of y column b = 10(3190) - (46)(590) 10(266) - (46)²

31900 - 27140 2660 - 2116

4760 544

b = 8.75

Y - Intercept Formula

a = y - bx

Where: a = y - Intercept y = Mean of Y column bx = Slope times the mean of X column

a = 59 - 8.75(x)

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