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Starnes, UPDATED The Practice of Statistics, 6e, Chapter 3
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Key Concepts:
Terms in this set (18)
Response variable
Measures an outcome of a study.
Explanatory variable
May help predict or explain changes in a response variable.
Scatterplot
Shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data set appears as a point in the graph.
positive association
Two variables have a positive association when values of one variable tend to increase as the values of the other variable increase.
negative association
Two variables have a negative association when values of one variable tend to decrease as the values of the other variable increase.
no association
There is no association between two variables if knowing the value of one variable does not help us predict the value of the other variable.
Correlation 𝓇
For a linear association between two quantitative variables, the correlation 𝓇 measures the direction and strength of the association.
Regression line
A line that models how a response variable y changes as an explanatory variable x changes. Regression lines are expressed in the form ŷ = a + bx where ŷ (pronounced “y-hat”) is the predicted value of y for a given value of x.
Extrapolation
The use of a regression line for prediction outside the interval of x values used to obtain the line. The further we extrapolate, the less reliable the predictions.
Residual
The difference between the actual value of y and the value of y, predicted by the regression line.
y intercept, Slope
In the regression equation ŷ = a + bx — a is the "y intercept", the predicted value of y when x = 0; b is the "slope", the amount by which the predicted value of y changes when x increases by 1 unit
least-squares regression line
The line that makes the sum of the squared residuals as small as possible.
residual plot
A scatterplot that displays the residuals on the vertical axis and the explanatory variable on the horizontal axis.
standard deviation of the residuals s
Measures the size of a typical residual. That is, s measures the typical distance between the actual y values and the predicted y values.
coefficient of determination r²
Measures the percent reduction in the sum of squared residuals when using the least-squares regression line to make predictions, rather than the mean value of y. In other words, r² measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.
high leverage
Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.
outlier
An outlier in regression is a point that does not follow the pattern of the data and has a large residual.
influential point
An influential point in regression is any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.
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