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Week 7 - Multiple Regression, testing for significance

Terms in this set (20)

Multiple regression extends the least-squares procedure to estimate 1)


2) to give us
1) B0 and B1 and B2 and Bk (and so on)


to give us the best possible prediction of Y from all the variables jointly
Multiple regression also referred to as
Ordinary Least Squares Regression
The least squares part refers to
the regression line minimizing the distance between the actual scores and predictor scores
B-weights are
The numbers (scores) that we multiply or weight each X variable to make a composite X that contains all the information from the seperate X scores in it
B-weights in MR instead of giving us a 1)___________ _____________

the b-weights in MR are 2)
1) Single slope

2) Partial slopes
each b tells us
1) how much change in predicting the Y score there will be for 1 unit change for that X score when all other X scores are held constant
This gives us a clue to how much each x is related to y when considering the ______________ ___________ the Xs
interrelationships among
Why is this better than looking at correlations among all variables separately?
they are not corrected for any correlation with each other
In regression - big R is the
association between linear composites of all the predictor variables and the outcome variable - in other words, the regression equation
In correlation - r describes the _________ relationship between two ________________ in a ___________________
the linear relationship between two variables in a sample
But - we usually want to make inferences about the relationship in a _______________
population
p =
Rho
Rho (p) is the
Correlation in the population

the population correlation coefficient
In correlation

Null states that rho =

I.e.,
0

i.e., there is no linear relationship between X and Y in the population
In correlation

Alternate states that rho


I.e.,
is not equal to 0

i.e., there is a linear relationship between x and y in the population
When correlation in the population is zero (i.e., null hyp is true) for a large enough sample, r will be
Normally distributed around 0
We ask ourselves - is our _________ correlation significantly greater than (or less than) _________?
Is our sample correlation significantly greater than (or significantly less than) zero?
Then we can now address the question as to whether
Is r large enough to conclude that there is a non-zero correlation in the population?

Or whether that correlation in the sample simply is just due to sampling error?
______________ correlations will be more likely to reject the null hypothesis and indicate that there actually is a relationship between the variables in the population
Large
A small point to note is that in correlations the little r refers to the correlation of the 1)___________ and rho refers to the correlation of the 2)_____________
1) Sample

2) Population
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