Business 205. Review Chi-Square Preview Regression.

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Presentation transcript:

Business 205

Review Chi-Square

Preview Regression

Linear Equations Straight line representation of an equation General formula Y = bX + a b is a constant (slope) a is a constant (Y-intercept)

Regression Finding the best-fitting straight line for a set of data Regression line The resulting straight line

Least-Squares Solution Best-fitting regression line will have the least squared error Best fitting line for the scatterplot data

Least-Squares Solution

Regression Equation Example You have the following data points in X and Y (X, Y) format and want to know the best fitting line for your data. Find the mean for each set of scores: M x = 5 M y = 6 XY

Regression Equation Example XYX - M x Y - M Y (X - M x )(Y - M Y )(X - M x ) – 5 = 211 – 6 = 52*5 = 10 (2) 2 = – 5 = -13 – 6 = -3-1*-3 = 3 (-1) 2 = – 5 = 15 – 6 = -11*-1 = -1 (1) 2 = – 5 = -24 – 6 = -2-2*-2 = 4 (-2) 2 = – 5 = 07 – 6 = 10*1 = 0 (0) 2 = 0 Sum of Product = 16 SS x = 10

Regression Equation Example

Plotting the Regression Line XY

Excel Regression Linest(y values, x values) Highlight 2 cells Type in the equation Ctrl+Shift+Enter 2 numbers appear Slope, y-intercept Intercept(y values, x values) Slope(y values, x values)