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chap14-a - Statistics Chapter 14 Introduction to Linear...

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Chap 14-1 Statistics Chapter 14 Introduction to Linear Regression and Correlation Analysis
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Chap 14-2 Chapter Goals After completing this chapter, you should be able to: Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant
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Chap 14-3 Chapter Goals After completing this chapter, you should be able to: Calculate and interpret confidence intervals for the regression coefficients Recognize regression analysis applications for purposes of prediction and description Recognize some potential problems if regression analysis is used incorrectly Recognize nonlinear relationships between two variables (continued)
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Chap 14-4 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 No causal effect is implied
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Chap 14-5 Scatterplots Scatterplots may be the most common and most effective display for data. In a scatterplot, you can see patterns, trends, relationships, and even the occasional extraordinary value sitting apart from the others. Scatterplots are the best way to start observing the relationship and the ideal way to picture associations between two quantitative variables.
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Chap 14-6 Looking at Scatterplots When looking at scatterplots, we will look for direction , form , and scatter . Direction: A pattern that runs from the upper left to the lower right is said to have a negative direction. A trend running the other way has a positive direction.
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Chap 14-7 Looking at Scatterplots (cont.) Figure 7.1 from the text shows a positive association between the year since 1900 and the % of people who say they would vote for a woman president. As the years have passed, the percentage who would vote for a woman has increased.
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Chap 14-8 Looking at Scatterplots (cont.) Figure 7.2 from the text shows a negative association between peak period freeway speed and cost per person of traffic delays. As the peak period freeway speed increases, the cost per person of traffic delays decreases.
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Chap 14-9 Looking at Scatterplots (cont.) Form: If there is a straight line ( linear ) relationship, it will appear as a cloud or swarm of points stretched out in a generally consistent, straight form. Example:
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Chap 14-10 Looking at Scatterplots (cont.) Form: If the relationship isn’t straight, but curves gently, while still increasing or decreasing steadily, we can often find ways to make it more nearly straight.
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Chap 14-11 Looking at Scatterplots (cont.) Form: If the relationship curves sharply, the methods of this book cannot really help us.
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Chap 14-12 Looking at Scatterplots (cont.)
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