# Shared Flashcard Set

## Details

Chapter 8 terms
Whats my line
11
Mathematics
01/18/2012

Term
 Model
Definition
 An equation or formula that simplifies and represents reality.
Term
 Linear model
Definition
 A linear model is an equation of a line. To interpret a linear model, we need to know the variables (along with their W's) and their units.
Term
 Predicted value
Definition
 The value of y found for a given x-value in the data. A predicted value is found by substituting the x-value in the regression equation. A predicted value are the values on the fitted line; the points (x,y) all lie exactly on the fitted line.
Term
 Residuals
Definition
 Residuals are the differences between data values and the corresponding values predicted be the regression model-or, more generally, values predicted by any model. Residual= observed value- predicted value= e=y-y
Term
 Least squares
Definition
 The least square criterion specifics the unique line that minimizes the variance of the residuals or, equivalently, the sum of the squared residuals.
Term
 Regression line (line of best fit)
Definition
 The particular linear equation (y=a+bx)that satisfies the least squares criterion is called the least squares regression line. Casually, we often just call it the regression line, or the line of best fit.
Term
 Slope
Definition
 The slope ,b, gives a value in "y-units per x-unit." Changes of one unit in x are associated with changes of b units in predicted values of y.
Term
 Intercept
Definition
 The intercept,a, gives gives a starting value in y-units. It is the y-value when x is 0.
Term
 Regression to the mean
Definition
 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.
Term
 Extrapolation
Definition
 Although linear models provide an easy way to predict values of y for a given value of x, it is unsafe to predict for values of x far from the ones used to find the linear models equation. Such extrapolation may pretend to see into the future, but the predictions should not be trusted.
Term
 Lurking variable
Definition
 A variable that is not explicitly part of a model, but affects the way variables in the model appear to be related. Because we can never be certain that observational data are not hiding a lurking variable that influences both x and y, it is never safe to conclude that a linear model demonstrates a casual relationship, no matter how strong the linear association.
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