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Chapter 3 Examining Relationships Lindsey Van Cleave AP Statistics September 24, 2006

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3.1: Scatterplots Scatterplot: shows the relationship between two quantitative variables, and each individual appears as a point in the plot. Explanatory Variable: explains the observed outcome. effect Response Variable: outcome of a study. cause

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Interpretting Scatterplots There are four things to look for when interpretting a scatter plot: –Direction: positive or negative –Outliers: falls outside the normal pattern –Form: linear, cluster, or gaps –Strength: how well the plot follows clear form Strong, moderately strong, weak, no relationship

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Examples of Scatterplots

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3.2 Correlation Correlation: measures the direction and strength of the linear relationship between two quantitative variables written as r. –*Correlation is not a complete description of two-variable data, even when the relationship between the variables is linear.

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Correlation Formula:

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Example:

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3.3: Least-Squares Regression Least-Squares Regression: method for finding a line that summarizes the relationship between two variables, but only in a specific setting.

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Coefficient of Determination: Coefficient of Determination: fraction of the variation in the values of y that is explained by least-squares regression of y on x.

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Facts about least-squares regression: 1. The distinction between explanatory and response variables is essential in regression. 2. A change of one standard deviation in x corresponds to a change of r standard deviations in y. 3. The least-squares regression line always passes through the point (x,y) 4. The square of the correlation, r, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.

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Residuals Residuals: plot the error (observed- predicted) of the LSRL. The shape of the plot can give some insight into our data. Four things to look for in residuals: –1. A pattern: especially curves –2. Increasing/Decreasing spread –3. Outliers –4. Extreme individual values of explanatory variable Good Residual Plot: –1. No pattern –2. Roughly equal number above and below 0 –3. constant spread

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Chapter 3 Dont even worry you can do most of this stuff on the calculator!!! Yay!

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Regression, Residuals, and Coefficient of Determination Section 3.2.

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