L6 - Simple Linear Regression.pptx

# L6 - Simple Linear Regression.pptx - Lecture 6 Linear...

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Lecture 6 Linear Regression and Correlation Analysis Chapter 14, Groebner 1

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Chapter Goals After completing this chapter, you should be able to: I. Calculate and interpret the simple correlation between two variables II. Calculate and interpret the intercept and gradient of a simple linear regression equation for a set of data III. Calculate coefficient of determination, R 2 and indicate if it’s a good fit data. 2
Scatter Plots and Correlation A scatter plot (or scatter diagram) is used to show the relationship between two variables Correlation analysis is used to measure strength of the association (linear relationship) between two variables Only concerned with strength of the relationship 3

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Scatter Plot Examples y y x y y x Linear relationships Curvilinear relationships x 4
Scatter Plot Examples y y x y y x Strong relationships Weak relationships (continued) x x 5

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Scatter Plot Examples y x y x No relationship (continued) 6
Correlation Coefficient, r Correlation measures the strength of the linear association between two variables The sample correlation coefficient, r is a measure of the strength of the linear relationship between two variables, based on sample observations (continued) 7

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Features of r Unit free Range between -1 and 1 The closer to -1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship If r > |0.5|, indicates strong relationship The closer to 0, the weaker the linear relationship 8
The Coefficient of Correlation, r 9 -1 -0.7 -0.3 0 0.3 0.7 1.0 Weak positive Weak negative Strong negative Moderate negative Strong positive Moderate positive

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r = +.3 r = +1 Examples of Approximate r Values y x y x y x y x y x r = -1 r = -.6 r = 0 10
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• Harpaljit Kaur

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