Simple linear regression fits a straight line to X-Y data
by the method of least squares.
The fit may then be used
to test the null hypothesis that
the slope is 0.
Assumptions:
The simple linear functionYi = b0 + b1*Xi + ei is the correct model,
where Yi is the ith observed value of Y, Xi
is the ith observed
value of X, and ei is the
error term. Equivalently, the expected value
of Y for a given value of X is b0 + b1*X.
The intercept is b0, the expected value of Y when X is 0.
the slope is b1, the amount by which the expected
value of Y increases when X increases by a unit amount.
The X variable (predictor variable) values are fixed
(i.e., X is not a random variable).
The Y variable (response variable) observations are
independent.
The variable Y is
normally distributed
with the same variance as the ei.
For a given value of X, the variable Y has constant mean.
The normality assumption is required for
hypothesis tests, but not for estimation.
The X variable is also known as the independent variable.
The Y variable is also known as the dependent variable.
Guidance:
Ways to detect before performing the
linear regression whether your data violate any
assumptions.
Ways to examine linear regression results to detect
assumption violations.
Possible alternatives if your data or
linear regression results indicate assumption violations.
To properly analyze and interpret the
results of simple linear regression, you should be familiar with the following terms and
concepts:
Failure to understand and properly apply
simple linear regression may result in drawing erroneous conclusions from your data.
If you are not familiar with these terms and concepts, you may wish to
consult with a statistician.
You may also want to consult the following references:
Brownlee, K. A. 1965. Statistical Theory and Methodology
in Science and Engineering. New York: John Wiley & Sons.
Daniel, Wayne W. 1995. Biostatistics. 6th ed.
New York: John Wiley & Sons.
Draper, N. R. and Smith, H. 1981.
Applied Regression Analysis. 2nd ed. New York: John Wiley & Sons.
Hoaglin, D. C., Mosteller, F., and Tukey, J. W. 1985.
Exploring Data Tables, Trends, and Shapes. New York: John Wiley & Sons.
Miller, Rupert G. Jr. 1996. Beyond ANOVA, Basics of Applied
Statistics. 2nd. ed.
London: Chapman & Hall.
Neter, J., Kutner, M.H., Nachtsheim, C.J., and Wasserman, W. 1996.
Applied Linear Regression Models. 3rd ed. Chicago: Irwin.
Neter, J., Wasserman, W., and Kutner, M.H. 1990. Applied
Linear Statistical Models. 3rd ed. Homewood, IL: Irwin.
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