Term

Definition
An equation or formula that simplifies and represents reality. 


Term

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

Definition
The value of y found for a given xvalue in the data. A predicted value is found by substituting the xvalue 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

Definition
Residuals are the differences between data values and the corresponding values predicted be the regression modelor, more generally, values predicted by any model. Residual= observed value predicted value= e=yy 


Term

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

Definition
The slope ,b, gives a value in "yunits per xunit." Changes of one unit in x are associated with changes of b units in predicted values of y. 


Term

Definition
The intercept,a, gives gives a starting value in yunits. It is the yvalue when x is 0. 


Term

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

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

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. 

