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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 ksamples 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 σ_{k}^{2} is
Mean Square within (MSW)

Assumptions for ANOVA
 a. ksamples are random and independent
 b.Each of the ksamples came from a normal population
 c. σ^{2}_{1}, σ^{2}_{2}, σ^{2}_{3}, ,σ^{2}_{k} are unknown but equal

The Statistical Linear Regression model is

SSxx or SSyy must always be...
positive

Sxy can be...
positive or negative

To Construct a (1 )100% Confidence Interval for unknown B, use
_{} , where

When solving for b in the estimated regression model...
write the equation out in general form first. If there it is "abx" that means "a+(b)x" which implies b is negative

The population correlation
denoted by 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 is
1<r<1

if r~1
we have a perfect relationship between x&y in a positive way. That is, if x increases, y increases.

if r~1
if x increases, y decreases. Or if x decreases, y increases

if r~0
the variables x&y are not related

Coefficient of Determination
denoted by for the population and r ^{2} for the sample. But or 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 r ^{2} the better it is.

The test statistic for Ho: is

If no value of is given, use

For sample correlation r, approximately equal to 1...
r≈1 for values of r>80% or .8

