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# Regression

### Chapters 7-10

Describe the association (in a scatter plot). • Direction, form, strength, unusual features • “In general, ____________.”
Interpret r. What is r? a measure of the strength and direction of a linear association.
Interpret r^2. % of the variation in (response variable) that is explained by the approximately linear relationship with (explanatory variable).
What is r2? a measure of the reliability / strength of a regression line
What is "s sub e?" standard deviation of the residuals
Interpret "s sub e." the typical size of the error when making a prediction
What do you do if there is an outlier or outliers? What do you do if there is an outlier or outliers? 1. Look for an explanation (e.g. typo? special circumstance?). 2. Calculate the regression model with and without it to determine its effect.
Describe an outlier If its x-value is inside of the range of the others, it’s internal and if it has a large residual, it might be changing just the y-intercept.
External outlier • x-value: outside of the range of the others • has leverage, the power to change the model o fits the pattern, then it will make model/pattern seem stronger than they really are. o doesn’t fit the pattern, then it will change the slope (influential).
Internal outlier • x-value: inside the range of the others • the further away it is from , the more it changes the slope (becomes more influential).
slope of the LSRL For every 1 unit increase in (the explanatory variable), our model predict an average increase of (SLOPE) units in (the response variable).
y-intercept of the LSRL • At (an explanatory variable) of 0 units, our model predicts (a response variable) of (Y-INTERCEPT) units. • Always determine whether or not this makes sense.
extrapolation • making a prediction for a value outside of the original range • Dangerous. Should try to avoid it.
Given r^2, find r. Use a square root. Then, determine whether it’s + of -.
Given only summary stats, find the LSRL. 1. Use r and the standard deviation to find slope. 2. Use the slope and the means to find the y-intercept. 3. Write the equation in slope intercept form. Remember to use meaningful variable names and proper notation.
Calculate a residual residual = observed or actual value MINUS the predicted value
positive residual the prediction was an UNDERESTIMATE
negative residual the prediction was an OVERESTIMATE
Created by: mrscowan