# Statistics Ch 5

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 Author: firefly501 ID: 137598 Filename: Statistics Ch 5 Updated: 2012-02-27 11:01:28 Tags: statistics Folders: Description: Regression Relationship between two variables Show Answers:

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1. Regression line
• a straight line that describes how a response variable y changes as an explanatory variable x changes. One variable explains or predicts the other.
• May be used to predict the value of y for a given value of x.
2. Least-squares regression line:
• the unique line such that the sum of the squared vertical
• (y) distances between the data points and the line is the smallest possible.
• 1. The distinction between explanatory and response variables is essential in regression.
• 2. There is a close connection between correlation and the slope of the least-squares line.
• 3. The least-squares regression line always passes through the point ( x , y )
• 4. The correlation r describes the strength of a straight-line relationship. The square of the correlation, r2, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.
4. Equation of least-squares regression line:
5. Coefficient of determination, r2
r2: the fraction of the variance in y (vertical scatter from the regression line) that can be explained by changes in x.
6. Residuals
dist. ( y - yˆ) = residual
7. Residual plots
• Residuals are the distances between y-observed and y-predicted. We plot them in a residual plot.
• If residuals are scattered randomly around 0, chances are your data fit a linear model, were normally distributed, and you didn’t have outliers.
• The x-axis in a residual plot is the same as on the scatterplot.
• The line on both plots is the regression line.
8. Outlier:
An observation that lies outside the overall pattern of observations.
9. Influential individual
• An observation that markedly changes the regression if removed.
• This is often an outlier on the x-axis.
10. Interpolation
• Making predictions
• The equation of the least-squares regression allows you to predict y for any x within the
• range studied. This is called interpolating.
11. lurking variable
• is a variable not included in the study design that does have an effect
• on the variables studied.
• It can falsely suggest a relationship.
12. Confounded variables
• Two variables are confounded when their effects on a response variable cannot be
• distinguished from each other. The confounded variables may be either explanatory
• variables or lurking variables.
13. Extrapolation
is the use of a regression line for predictions outside the range of x values used to obtain the line.

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