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Unformatted text preview: SOCIOLOGY 005 Lecture 6 Correlation and Regression By doing things the easy way, we were quickly able to determine whether or not the variation in Y is signifcantly related to X We were also able to quickly calculate R 2 and Pearson’s r But the Shortcuts we took are not without cost • These only work with bivariate regression (converting r to R 2 ) • We don’t have a clear idea about what error really is • Our measure oF model ft told us nothing about the regression line itselF in terms oF inFerence and confdence intervals We must now look at error and the Form oF a regression equation in more detail Correlation and Regression IF there was an a strong linear law in which only education aFFected number oF crimes committed, our previous equation would re¡ect it. Y = a + bX Predicted Values and Error ˆ Y = a + bX UnFortunately, Education is but one Factor which might be related to crime and as such we are likely to commit error trying to predict Y using X. This being the case, the real value For Y is not predicted and instead we typically note that the predicted value For Y is just that - A Predicted Value Although we adjusted the equation to refect that Y is a predicted value, we are still interest in the actual value For Y We can compare the predicted value oF Y to the actual value oF Y in order to better understand the relationship between X and Y This allows us to calculate the amount oF error we made when predicting Y e i = Y i ! ˆ Y i Predicted Values and Error Since we are now taking error into account, we can rewrite our Formula so the actual value oF Y is predicted Y = a + bX + e This new equation is the Formula For the linear regression model Predicted Values and Error Once we have calculated an error term For each case, we can use this distribution oF errors in much the same way we have used value oF X or Y to calculate Sums oF Squares or Variance Just like any other time we’ve calculated the average For d on either the DV or IV, the mean score For the error terms is 0 We can think oF the regression line we construct as being the one line which minimizes most the amount oF error we create when trying to predict Y using X Predicted Values and Error IF you remember the regression we previously conducted, the relationship between education and crime could be expressed in the Following equation Y = 9.242 + ( ! .425) X Predicted Values and Error We can now use our knowledge of...
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This note was uploaded on 10/23/2011 for the course SOC 10 taught by Professor Dunn during the Spring '10 term at UC Riverside.
- Spring '10