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The coefficient of determination,
r^2
, measures the
proportion of variability in y that is explained by x. Each SRS is drawn from a distinct
subpopulation (explanatory variable). One SRS, with multiple measurements (fixed x
value)
y^= bo + b1x
µy= ßo + ß1x
(where ß1= µb1)
yi= ßo + ß1x + ei
(0, ∂)

Linearity
as µy connects subpopulation means.

Constant spread
∂ doesn’t depend on x.

Normality
 Each is bell shaped within a subpopulation.
Formulas for regression standard error s and SEb1 are given.
Ho: ß1= 0 (Ha would be 1 or 2 sided)
t= b1/SEb1 (n2 degrees of freedom)
CI b1 + tSEb1
NOTE on robustness A moderate lack of normality may be tolerated but outliers may be
problematic.
r is the sample correlation, p is the population correlation.
Ho: p= 0 (against Ha 1 or 2 sided)
 Calculate other form of test statistic t and use n2 df.
Confidence interval for y^
(estimate from µy= ßo + ß1x.)
y^ + tSEµ^
Predicted interval for y^
(prediction for y)
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This note was uploaded on 02/27/2011 for the course STAT 2120 taught by Professor Jeffreyholt during the Fall '10 term at UVA.
 Fall '10
 JEFFREYHOLT
 Statistics, Coefficient Of Determination, Linear Regression

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