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Unformatted text preview: • The due date for this homework is 2 March. • Read Chapter 11. • See Blackboard for assignment. Chapter 11: Homework • You should be able to recall: – The meaning of different symbols used in regression (Y, X, β , β 1 ) – What is meant by “significance of regression” – What is meant by “residual” – What is meant by “coefficient of determination” – What is meant by “correlation coefficient” • You should be able to accomplish: – Conduct a simple linear regression. – Find the variance of the residual error in regression output. – Conduct hypothesis tests for parameters of linear regression – Conduct confidence intervals on parameters of linear regression – Make predictions of future observations based on a linear regression – Apply methods used to transform nonlinear data to be linear • You should be able to understand: – What is meant by “least squares estimate” – How to interpret residual plots – What is meant by “outliers” and what should be done with them – How to interpret regressions on transformed data – The difference between correlation and regression Chapter 11: Objectives • This chapter is about regression. • Regression, although based on the same math used for hypothesis testing, is used for an entirely different purpose. • It is important to remember this because the line between regression and hypothesis testing is going to be blurred later on in the semester. • Whereas hypothesis testing is used to test parameters of one or two populations based on a sample, regression is used to identify a relationship between two or more variables . • For this chapter and the next one, the relationship in which we are interested is a linear relationship. Chapter 11: Overview • For this chapter and the next one, the relationship in which we are interested is a linear relationship. • Which of these is linear and which is not? Chapter 11: Linearity ( 29 2 5 9 0.2 2 3 6 0.05 30 1 10 y x y x x y x y x y x = + = + = = = • Linear means that y is proportional to x; that a straight line can be drawn to describe their relationship to one another. Which of these plots seem to show a linear relationship? Chapter 11: Scatterplots X Y 16 14 12 10 8 6 4 2 140 120 100 80 60 40 20 Scatterplot of Y vs X X2 Y2 16 14 12 10 8 6 4 2 200 150 100 5050100 Scatterplot of Y2 vs X2 X3 Y3 16 14 12 10 8 6 4 2 250 200 150 100 50 Scatterplot of Y3 vs X3 X4 Y4 16 14 12 10 8 6 4 2 20 101020 Scatterplot of Y4 vs X4 a b c d ? • This chapter is about how we draw the best line through the data seen on a scatterplot, how to test whether our parameters are statistically significant, how to test whether the regression itself is statistically significant, and how to tell the quality of the fit. It also discusses a related (but separate ) concept called correlation....
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 Spring '08

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