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Chapter 7: Linear Regression
This covers all the terms from Chapter 8, as well as some additional terms in the "What Have We Learned?" section. Note that the symbol y^ is y with a triangle-shaped line over it. The symbol y^- is y with a horizontal line above it; same for x.
Terms in this set (12)
Slope of the line
Provides a value in "y-units per x-unit."
(Formula: b1= rsy/sx, where 1,s, and x are subscripts)
An equation/formula that simplifies and represents reality.
Equation of a line; to interpret, we must know the variables (along with their W's) and their units.
Value of y^ found for a given x-value in the data; found by substituting the x-value in the regression equation; these are the values of the fitted line- the points (x, y^) all lie exactly on the fitted line
Differences between data values and the corresponding values predicted by the regression model- or, more generally, values predicted by any model ( =observed value- predicted value=e=y-y^)
This criterion specifies the unique line that minimizes the variance of the residuals or, eventually, the sum of the squared residuals
Regression to the mean
Because the correlation is always less than 1.0 in magnitude, each predicted y^ tends to be fewer SDs from its mean than its corresponding x was from its mean.
Regression to the line of best fit
Particular linear equation (y^=bo=b1x (o and 1x are subscripts)) that satisfies the least squares regression line. Casually, we often just call it the regression line, or the line of best fit.
b1 (1 is subscript) 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. The slope can be found as the slope of the correlation.
gives a starting value in y-units; at the y^ value x is 0. Formula (b0= y^- - b1x^-)
se (e is subscript)
Standard deviation of residuals is found by se= (square root of Σe^2/n-2); when assumptions and conditions are met, the residuals will be described by this SD and the empirical rule.
R^2 is the square pf the correlation between y and x; gives fraction of variability of y accounted for by the least squares linear regression on x
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