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Inference for Linear Regression (C27 BVD)
* If we believe two variables may have a linear
relationship, we may find a linear regression
line to model that relationship.
* But, if we do not have the entire populations
for both variables, we may sample from the
population and find a sample regression line
using procedures we already learned.
* Mainly we would look at the slope as a good
indicator of a linear relationship – if there is no
linear relationship the slope for the population
regression line should be 0.
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* Linear – check the scatterplot for a straight
relationship and residual plot for no patterns.
* Independent – 10% condition (sample is no more
than 10% of population)
* Normal – Make a histogram or NPP of residuals to
make sure there is no strong skew.
* Equal Variance – The amount of scatter of residuals
should be roughly the same (no fanning).
* Random sampling/assignment
*
* The sampling distribution for slope is unimodal
and symmetric and if conditions are met a tdistribution is an appropriate model.
* The interval is b +/- t* sr/(sx sqrt(n-1))
* Where sr is std dev of residuals and df = n-2
and the whole denominator is SE.
* Use LinRegTInt on calculator
*
* Usually H0 is that B0
= 0 (remember: use Greek
(Beta) for parameters for the population)
* Can be one or two-tailed alternate.
* Test statistic t =(b – B0)/SE
* Can use t-table for df = n-2
* Use LinRegTtest on calculator
* On calculator test where you choose alternate, you
will see both Beta and Rho, the population
correlation coefficient. Testing for zero slope works
the same as testing for zero correlation so the
calculator just does both.
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