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Political Science
Joseph Fletcher

Tuesday January 11, 2011 Regression equation: y = a + bx y = the predicted value, or the dependent variable and x = the independent variable a = intercept (y when x = 0 ) b = the slope of a line were going to discuss this more next week regression and correlation fit together in a way, since correlation is defined by a regression equation people think interval data is more powerful than nominal or ordinal.... bivariate analysis: if we want to predict y from x the scores from x must be at least as efficient as the scores of y as the mean of y itself. So we have two axes and the idea is that theres one independent and one dependent variable. These variables have ranks that some things are higher than others, and that theres a constant interval between each of the units. Its measured in some set of units i.e. x = years of education. Now the idea here is that we can have a number of individual cases that are ranked on x or ranked on y. the best predictor of y (just y, alone) would be whatever the mean score of y is. and the reason that it s the best predictor is that y would give us the smallest average deviation of the mean of y. so the mean of the sample becomes the standard of which we compare any other variable. so the square deviation of the mean score will let us decide if x is useful. pg. 309 in brians (only just touched upon on that page). theres more than one kind of variance or variation. in fact theres 3 we need to worry about... Types of Variation 1) Total Variance - It equals the sum of the square differences from the mean on any variable - The average squared deviation = the total variation of the y variable - The least squares line 2) Unexplained Variance - Everything thats left over (that doesnt touch the regression slope aka the equation y = a + bx) 3) Explained Variance - Total variation of y that can be attributed to the influence of x - Pearsons correlation = the square root of the variance. - So r = the square root of explained variance.
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