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Chapter 8: Linear Regression
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Terms in this set (11)
Model
An equation or formula that simplifies and represents reality
Linear Model
An equation of a line. To interpret a linear model, we need to know the variables along with their W's and their units.
Predicted Value
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 poins (x,yhat) all lie exactly on the fitted line.
Residuals
The difference between data values and the corresponding values predicted by the regression model- or, more generally, values predicted by any model
Residual = observed value - predicted value
Least Squares
Specifies the unique line that minimizes the variance of the residuals, or, equaivalently, the sum of the squared residuals.
Regression to the Mean
Because the correlation is always les than 1.0 in magnitude, each predicted y-hat tends to be fewer standard deviatiions from its mean than its corersponding x was from its mean.
Regression Line
Line of Best Fit
The particular linear equation
y-hat = b-not + b1x
that satisfies the least squares criterion. Casually, we often just call it the regression line, of the line of best fit.
Slope
The slope, gives a value in y-units per x-unit. Changes of one unit in x are associated with the changes of b1 units in predicted values of y.
Intercept
The intercept, b0, gives a starting value in y-units. Its the y(hat)- value when x is 0.
se
The standard deviation of the residuals. When the assumption and conditions are met, the residuals can be well described by using the standard deviation and the 68-95-99.7 Rule
R2
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.
An overall measure of how successful the regression is in linearly relating y to x
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