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15 Cards in this Set
- Front
- Back
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Fitted Value |
¤ Ŷ =Y-hat |
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Errors or Residuals |
¤ e= Y – Ŷ |
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minimizing errors |
1) summing the errors: positive and negative errors are equally bad 2) to avoid cancellation of positive errors by negative errors, square the errors and add them up: called the Sum of Squared Errors (SSE ) |
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Least Squares |
combination of b0 and b1 that minimize the Sum of Squared Errors (SSE) |
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Thing 2 Formula |
DY= bj *DXj use to make predictions or forecasts |
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Degrees of Freedom |
df = n – k – 1 number of independent pieces of info involving the response data that are needed to calculate the sum of squares, where n is the number of observations and k is the number of predictor variables. |
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Sum of Squared Errors (SSE) |
each error is the actual value of the dependent variable minus the fitted value. e = Y - Ŷ |
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Mean Squared Error (MSE) |
SSE/(n-k-1) An estimate of the regression model's variance. |
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Total Sum of Squares (SST) |
the sum of the squared differences between the actual value of the dependent variable and its mean value. |
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Standard Error of the Estimate (SEE) |
Square root of MSE An estimate of the regression model's standard deviation so the Margin of Error is ±2 SEE with 95% confidence |
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coefficient of determination (R^2) |
1-SSE/SST The percentage of the response variable's variation that is explained by its relationship with 1 or more predictor variables. In simple regression, the correlation r=± square root of R^2 |
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SEE is the standard error of estimate |
- SEE is in the same units as the dependent variable - The margin of error is approximately SEE |
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R^2 is the coeficient of determination |
- Relative measure of fit: ¤0% ≤ R2 ≤100% - Percent of total variation explained by the equation - Perfect Fit: R2 =100% |
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Correlation r is an index of linear association |
* 1≤ r ≤ +1r near zero means 2 variables are uncorrelated or there is no linear relationship between them * association: positive or negative; weak or strong *correlation: standardized Covariance |
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Correlation vs. Regression |
* Index vs. Equation * Correlation r vs. R^2 fit measure |
