Chapter 11:
Regression Analysis I (11.1-
11.3)
Simple Linear Regression
A positive slope means
E(y) increases by the
amount B1 for each unit
increase in x
Intercept
is the
estimated avg value of Y when x=0;
slope measures the estimated change in the avg. value of Y as a result of a 1
unit
change
Multicollinearity:
A condition occurring when two or more independent variables in the same regression model
can predict each
other better than the dependent variable.
Standard error of estimate: variability of the observed y values from the predicted values
A high R^2 means a strong relationship between the independent and dependent variables
In least-squares regression, best fitting line minimizes the sum of squares of the observed errors
A confidence interval for the independent variable x would specify the uncertainty about the mean value of the
dependent variable
R^2 is the sample correlation coefficient; ex: .2645, 26.45% of the variation in y can be explained by x
Correlation:
How
strong the relationship is.
Coefficient correlation: r, ranges from -1 to 1, sign is the
same as slope, measures degree of association, no
indication of cause and effect relationship
Confidence
intervals: C.I
estimate of
expected
value of y,
will be narrower then
prediction interval
for x.

Chapter 12:
Multiple Regression
A)
Test parameter significance: shows if there is a
linear
relationship between all x
variables together and y
Overall all: H0: B1=B2-B3=0 (no linear relationship); Ha: at least one coeff is
not 0
Individual: H0:
Bi=0; Ha: Bi =/ 0 or
(<,>); test stat= t
B)examine variation
measures: proportion of variation in y explained by all x variables taken together

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- Spring '08
- Deshmikh
- Slope, Linear Regression, Regression Analysis, regression model, Forecast error, independent variables