Lecture10.chapt2andsec10.1

Lecture10.chapt2andsec10.1 - Lecture 10, Chapter 2 &...

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Looking at Data - Relationships We will now look at determining an association or relationship between two quantitative variables. To study the relationship we measure both variables on the same unit or individual. Two variables are associated if some values of one variable tend to occur more often with certain values of the second variable. But there is a caution: the relationship between two variables can be strongly influenced by other variables lurking in the background. A response variable, also called the dependent or “Y” variable, measures an outcome of a study. An explanatory variable, also called an independent or “X” variable, explains or causes these changes. Examples: Page 1
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Use the following procedure to examine the relationship between two quantitative variables: 1. Graph the relationship, usually a scatterplot . Describe the form, direction, and strength. Look for outliers. 2. Look at the correlation to get a numerical value for the direction and strength. 3. If the data is reasonably linear, get an equation of the line using least squares regression. 4. Question, association does not imply causation. Look at the residual plot to see if there are any outliers or the possibility of lurking variables. 5. Look at the normal probability plot to determine whether the residuals are normally distributed. (The dots sticking close to the 45 degree line is good.) 6. Look at hypothesis tests for the correlation, slope, and intercept . Look at confidence intervals for the slope and intercept. 7. If you had an outlier, you should re-work the data without the outlier and comment on the differences in your results. Scatterplots: A scatterplot shows the relationship between two quantitative variables measured on the same unit/individual. By convention, the explanatory (independent) variable is plotted on the x-axis and the response (dependent) variable is plotted on the y-axis. Page 2
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1. Look at the overall pattern. The overall pattern can be described by form, direction and strength. Form: is the scatterplot linear, quadratic, etc. Direction: is the association positive or negative? Note: Two variables are positively associated when above average values of one variable tend to accompany above-average values of the other and below-average values also tend to occur together. Two variables are negatively associated when above average values of one accompany below-average values of the other, and visa versa. Strength: of the relationship. 2. Look for striking deviations from the overall pattern. An important deviation is an outlier, an individual value that falls outside the overall pattern.
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This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lecture10.chapt2andsec10.1 - Lecture 10, Chapter 2 &...

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