Error 21667 14125 1046 269 standardized coefficients

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Unformatted text preview: ted variables entered. b. Dependent Variable: final exam scores (out of 100) Model Summaryb Model 1 R .889a Adjusted R Square .738 R Square .791 Std. Error of the Estimate 8.24671 a. Predictors: (Constant), exam 2 scores (out of 75) b. Dependent Variable: final exam scores (out of 100) ANOVAb Model 1 Regression Residual Total Sum of Squares 1027.967 272.033 1300.000 df 1 4 5 Mean Square 1027.967 68.008 F 15.115 Sig. .018a a. Predictors: (Constant), exam 2 scores (out of 75) b. Dependent Variable: final exam scores (out of 100) Coefficientsa Model 1 (Constant) exam 2 scores (out of 75) Unstandardized Coefficients B Std. Error 21.667 14.125 1.046 .269 Standardized Coefficients Beta a. Dependent Variable: final exam scores (out of 100) Predicted y = y-hat = 21.667 + 1.046(x) 191 .889 t 1.534 3.888 Sig. .200 .018 Inference in Linear Regression Analysis The material covered so far is presented in Chapter 3 and focuses on using the data for a sample to graph and describe the relationship. The slope and intercept values we have computed are statistics, they are estimates of the underlying true relationship for the larger population. Chapter 14 focuses on making inferences about the relationship for the larger population. Here is a nice summary to help us distinguish between the regression line for the sample and the regression line for the population. Regression Line for the Sample Regression Line for the Population Aside: E(Y) = Y(x) = mean response at a given x; sometimes called the regression function. It can take on many forms, we will consider the simple linear regression function: 0 + 1x 192 To do formal inference, we think of our b0 and b1 as estimates of the unknown parameters 0 and 1 . Below we have the somewhat statistical way of expressing the underlying model that produces our data: Linear Model: the response y = [0 + 1(x)] + = [Population relationship] + Randomness This statistical model for simple linear regression assumes that for each value of x the observed values of the response (the population of y values) is normally distributed, varying around some true mean (that may depend on x in a linearway) and a st...
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This document was uploaded on 02/25/2014 for the course STATS 250 at University of Michigan.

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