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22 Cards in this Set
- Front
- Back
- 3rd side (hint)
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variable relationships
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variables are associated if knowing the value of one variable tells you something about the other variable
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ex: if it's a boy, it's not a girl
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response variable
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measures an outcome of a study
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dependent variable (y)
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explanatory variable
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explains or causes changes in a response variable
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independent variable (x)
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scatterplots
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show the relationship between the two quantitative variables for the same individuals
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plot values of one variable on x and other on y
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direction - positive association
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on avg, an increase in one variable increases another variable
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direction - negative association
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on avg, a decrease in one variable decreases another variable
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correlation (r)
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measures the direction and strength of a linear relationship between two quantitative variables
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correlation properties - variables
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doesn't matter what variable is x or y, doesn't tell which variables are expl. or resp., both must be quantitative, correlation has no units
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correlation properties - association
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positive (r) indicates positive association, negative (r) indicates negative association
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correlation properties - range
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ranges from -1≼r≼1; close to 0 - weak relationship, close to 1 - strong + trend, close to -1 - strong - trend, if r=∓1, then data lies on a straight line
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regression line
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straight line that describes how response (y) changes as explanatory (x) changes
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prediction
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use regression line to predict outside range of data
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extrapolation
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using regression line to predict outside the range of data
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may or may not be a good prediction based on accuracy of regression
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Least Square Regression line ("y on x")
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the line that minimizes the sum of squares of the vertical distances between line and data points
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interpreting the regression line
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always passes through (x̄, y bar)
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square of the correlation
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r²=variance of predicted values ŷ/variance of actual values y
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residual
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error between the real value and estimated value
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y=ŷ-e
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residual plot
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scatterplot of the residuals (y-axis) vs explanatory variable (x-axis)
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help us determine if LSR is good fit...if data is randomly placed around line y=0, LSR is good fit
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outlier
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observation that lies outside the overall pattern
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outliers in (y) direction have large residuals but other outliers may not have large residuals
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influential observation
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observation that drastically changes the statistical calculations if it is removed
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outliers in (x) direction are influential
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lurking variable
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variable that is neither explanatory or response in your study, but influences those variables
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can falsely suggest a relationship
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restricted range problem
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data set doesn't contain the full set of values that can happen
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can produce misleading results
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