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Simple Linear Regression Analysis


This chapter has discussed simple linear regression analysis, which relates a dependent variable to a single independent (predictor) variable. We began by considering the simple linear regression model, which employs two parameters: the slope and y intercept. We next discussed how to compute the least squares point estimates of these parameters and how to use these estimates to calculate a point estimate of the mean value of the dependent variable and a point prediction of an individual value of the dependent variable. Then, after considering the assumptions behind the simple linear regression model, we discussed testing the significance of the regression relationship (slope), calculating a confidence interval for the mean value of the dependent variable, and calculating a prediction interval for an individual value of the dependent variable. We next explained several measures of the utility of the simple linear regression model. These include the simple coefficient of determination and an F test for the simple linear model. We concluded this chapter by giving an optional discussion of using residual analysis to detect violations of the regression assumptions. We learned that we can sometimes remedy violations of these assumptions by transforming the dependent variable.











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