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CHAPTER 14 - SIMPLE LINEAR REGRESSION - Coggle Diagram
CHAPTER 14 - SIMPLE LINEAR REGRESSION
ERROR TERM E
in a regression analysis the error term e is a random variable
has a mean or expected value of 0
required assumptions
the variance of the error term is the same for all values of X
the values of the error term are independent
the error term is normally distributed
COEFFICIENT OF DETERMINATION
R^2
cannot be negative
COEFFICIENT OF CORRELATION
can be either negative or positive
the value of the coefficient of correlation (R) can be equal to the coefficient of determination (R^2) if R^2 = 0 or 1
REGRESSION MODEL
y=B0 + B1X + e
the equation that describes how the dependent variable is related to the independent variable
REGRESSION EQUATION
E(y) = B0 + B1x
ESTIMATED REGRESSION EQUATION
the model developed from the sample data that has the form yhat = b0+b1x
b1 = the slope
b0 = y intercept
MEAN SQUARE ERROR
the unbiased estimate of the variance
MSE
the standard error is the square root of MSE
REGRESSION ANALYSIS
a statistical procedure for developing a mathematical equation that describes how one dependent and one or more independent variables are related
the variable that is being predicted is the dependent variable
LEAST SQUARES LINE
larger values of r^2 imply that observations are more closely grouped about the least squares line