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# Regression 1003

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This 0 page Study Guide was uploaded by Upasana Raja on Monday December 7, 2015. The Study Guide belongs to 1003 at a university taught by Jennifer in Fall 2015. Since its upload, it has received 39 views.

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Date Created: 12/07/15

Regression Regression allows researchers to 1 Examine the nature and strength of the relationship between variables 2 The relative predictive power of several lV s on a DV 3 The unique contribution of one IV on the DV when controlling for the effects of other covariates when applicable Similar to a one way vs factorial ANOVA Similar to a oneway ANOVA a simple regression involves a single independent variable now called a predictor variable and one dependent variables now called an outcome variable Similar to a factorial ANOVA in that a multiple regression involves multiple predictor variables multiple lV39s Most closely related to a correlational coef cient However in a correlational coef cient there is not designation between a predictor variable and an outcome variable it is simply variables x and y Regression always indicates which variable is the predictor and which is the outcome variable Again a simple linear regression is similar to a correlation When examining the relationship between 2 variables you can use either test However regression provides more information 1 Yields more information about your variables 2 Allows you to think about the relationship of the variables in more detail more than just whether they are related You can estimate the value on based on the known value of X Purpose To make predictions about the value of the dependent variable given certain values of the predictor variable IV Basically you are predicting the value of the DV based on the value of the IV This is a simple extension of the correlation Not necessarily better than a correlation but gives you a different way of conceptualizing your question If I were interested in the relationship between studying and test scores I can use simple regression to answer the following question If I know how much time a student studies for a test what would I predict their test grade to be This will depend of the strength of the correlation stronger correlations will have strong predictive power or accurate predictions Most researchers are interested in multiple regression Similar to a factorial ANOVA as it involved multiple predictor variables and one outcome variable So suppose I am not only interested in how much studying a student does and how it impacts their test grade but now I am also interested in how much sleep the student gets the night before and how often they came to class in the last month three predictor continuous variables Allows you to do several things 1 Determine how all of the predictor variables as a group impact the dependent variable 2 Determine the impact of each predictor variable impacts the DV which controlling for the other predictor variables 3 The relative strength of the predictor variable 4 Whether there are interaction effects between the predictor variables As with a correlation regression variables both IV and DV need to be measured on a interval or ratio scale continuous variables Dichotomous variables categorical variables with 2 responses eg yesno can also be used as the predictor variable Note these dichotomous variables can be used as the DV but this involves a much more complex test The assumption Two variables are linearly related as one variable increases there is a corresponding increase in the other variables The Simple Linear Regression Equation Y bX a Y the predicted value of the Y variable b the unstandardized regression coef cient and the slope of the regression line X the value of the X variable a the value of the intercept where the regression line crosses the y axis Regression Coef cient A measure of the relationship between each predictor variable and the DV In simple linear reoression The slope of the regression line In multiple reoression the various regression coef cients combine to create the slope of the regression line br SX b the regression coef cient r the correlation between x and y Sy the SD of the Y variable Sx the SD of the X variable This will simply tell us exactly where the regression line crosses the yaxis Essentially tells you what the Y value will be when the X value is equal to 0 azY hY Y the average value of Y X the average value of X b the regression coef cient The Multiple Regression Equation Y a bX1 bX2 Y the predicted value on DV X1 the value of the rst predictor variable X2 the value of the second predictor variable Unique Variance the proportion of variance in the DV explained by one predictor variable when controlling for the other39s Multicollinearity The degree of overlap among predictor variables in a multiple regression Can be a problem when high in determining unique relations among an IV and the DV After we collect our data we input that data into a scatterplot a graphic representation of the data along two dimensions X and Y After preparing the scatterplot we can create a regression line also known as the line of best t the line that can be drawn through the scatterplot that best quotfitsquot the data We know that our predictions will not be perfect Some data points will be closer to the regression line than others Residual Error in prediction The difference between the actual value on and the predicted value of Y We can overpredict negative residual and underpredict positive residual the Y value

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