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| an equation or formula that simplifies and represents reality |
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| an equation of a line; to interpret a linear model, we need to know the variables and their units |
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| the value of y-hat found for a given 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-hat) all lie exactly on the fitted line |
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| residuals are the differences between data values and the corresponding values predicted the regression model - or, more generally, values predicted by any model |
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| 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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| because the correlation is always less than 1.0 in magnitude, each predicted y-hat tends to be fewer standard deviations from its mean than its corresponding x was from its mean |
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| the particular y-hat = b0 + b1x that satisfies the least squares criterion |
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| the slope, b1, 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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| b0 gives a starting value in y-units; y-hat value when x is 0 |
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| the standard deviation of the residuals |
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| square of the correlation between y and x; gives the fraction of the variability accounted for by the least squares linear regression on x |
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