 | Term | Definition |
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Model |
an equation or formula that simplifies and represents reality |
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linear model |
a linear model is an equation of the form: (y^) = b0 +b1(x); to interpret a linear model we need to know the variables (along with their W's) and their units |
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residuals |
residuals are the difference between data values and the corresponding values predicted by the regression model -- or, values predicted by any model; residual = observed value - predicted value = y - (y^) |
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predicted value |
the value of (y^) found for each x-value in the data; a predicted value is found by substituting the x-value in the regression equation; the predicted values are the values on the fitted line; the points (x, (y^) all lie exactly on the fitted line |
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slope |
the slope gives a value in "y-units per x-unit"; changes of one unit in x are associated with changes of b1 units in predicted values of y |
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regression to the mean |
because the correlation is always less than 1.0 in magnitude, each predicted (y^) tends to be fewer standard deviations from its mean than its corresponding x was from its mean. this is called regression to the mean |
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regression line [ line of best fit ] |
(y^) = b0 + b1(x); the particular linear equation that satisfies the least squares criterion is called the least squares regression line |
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intercept |
the intercept, b0, gives a starting value in y-units; its the (y^)-value when x is 0 |
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least squares |
the least squares criterion specifies the unique line that minimizes the variance of the residuals or, equivalently, the sum of the squared residuals |
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r^2 |
is the square of the correlation between y and x; gives the fraction of the variability of y accounted for by the least squares linear regression on x; is an overall measure of how successful the regression is in linearly relating y to x |
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