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analysis of the equational relationship between X and Y. |
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ß1 has a t distribution which standardizes its value to see if it is significantly different from 0. |
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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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Correlation analysis is the study of the nature and degree of the relationship between variables. Extrapolation is using Xs beyond the range of the given Xs to predict Y. This can cause large errors in prediction. Relationship of slope to the correlation coefficient: signs are the same. |
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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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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. Stepwise 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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when there are too many predictors and not enough samples. |
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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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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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