Ch 12 &13
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Analysis of Variance (ANOVA)
A procedure used to test the Null Hypothesis that the means of three of more populations are equal.
The grand mean for all k-samples is
SST, SSB AND SSW must always be...
positive, since it's they're the sum of squares
The point estimator for the unknown common variance σk2 is
Mean Square within (MSW)
Assumptions for ANOVA
- a. k-samples are random and independent
- b.Each of the k-samples came from a normal population
- c. σ21, σ22, σ23, ,σ2k are unknown but equal
The Statistical Linear Regression model is
SSxx or SSyy must always be...
Sxy can be...
positive or negative
To Construct a (1-
)100% Confidence Interval for unknown B, use
When solving for b in the estimated regression model...
write the equation out in general form first. If there it is "a-bx" that means "a+(-b)x" which implies b is negative
The population correlation
and defined as the strength of the relationship between two variables, x&y.
The sample correlation
denoted by r. Since the population correlation Rho is usually unknown, the point estimator of the population correlation is the sample correlation r.
The range for
we have a perfect relationship between x&y in a positive way. That is, if x increases, y increases.
if x increases, y decreases. Or if x decreases, y increases
the variables x&y are not related
Coefficient of Determination
for the population and r2
for the sample. But
is usually unknown. The coefficient of determination for the samples represents the % of variation
in the dependent variable y, explained by the independent variable (x) in the extimated least squares regression model ŷ
. The higher the value of r2
the better it is.
The test statistic for Ho:
If no value of
is given, use
For sample correlation r, approximately equal to 1...
r≈1 for values of r>80% or .8
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