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analysis of the equational relationship between X and Y. |
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, has a t distribution which standardizes its value to see if it is significantly different from 0. |
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, ß0, is not interpreted. |
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,r, indicates direction and strength of the LINEAR relationship between X and Y. |
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Coefficient of Determination |
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R2, the ratio of explained variation in Y to the total variation. |
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will be smaller for better predictive equations. |
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is the study of the nature and degree of the relationship between variables. |
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is using Xs beyond the range of the given Xs to predict Y. This can cause large errors in prediction. |
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Relationship of slope to the correlation coefficient |
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when Xs are highly correlated this gives redundant information. |
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- non-constant variance in the residuals |
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atypical values in a data set. |
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Non-linear relationships- |
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curvilinear patterns or logarithmic relationships |
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Multiple regression analysis |
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includes one dependent variable and more than one independent. |
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tries all combinations of variables and produces the best predictors in order of their predictive power. |
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Artificially Inflated R-squared |
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occurs when there are too many predictors and not enough samples. |
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should produce a nearly straight line without outliers. |
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T distribution vs. F distribution |
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: t is used to test the individual coefficients where F tests the overall model. |
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Residuals are the differences in the observed value of Y at a given X and the predicted value. |
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should fall within +/- 3 in order to be considered normal values. |
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