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Linear Regression and Correlation
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Statistics
Linear Regression and Correlation
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14 Terms
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1
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population
Muy=alpha+Bx
2
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sample
y-hat=a+bx
3
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sampling distribution of b
unimodal curve
N(0, sigma\*b → sigmaSEb)
4
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statstic
y-int a
slope b
SD of residuals S
SD of slope SEb
5
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parameter
y-int alpha
slope B
SD of residuals sigma
SD of slope sigma b
6
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Confidence Intervals for Slope 1) state:
parameter: true slope of the population
LSRL for x context vs. y context
statistic = b
confidence level
7
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Confidence Intervals for Slope 2) plan:
Linear: The scatterplot needs to show a linear relationship. Also, the residual plot doesn’t have a leftover curved pattern.
Independent: 10% rule
Normal: A dot plot of the residuals cannot show strong skew or outliers
Equal SD: The residual plot does not show a clear sideways Christmas tree pattern
Random
8
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Confidence Intervals for Slope 3) do:
By Hand
b+-t\*SEb
t\* = invT (tail %, df (n-2) use positive slope
__OR__ LinRegTInt
9
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Confidence Intervals for Slope 4) conclude:
We are % confident that the interval (*,*) captures the true slope of x-int v. y-int.
10
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Significance Test for Slope 1) state:
parameter in context
H0, Ha
alpha
11
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Significance Test for Slope 2) plan:
1 sample t-test (for slope)
LINER
12
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Significance Test for Slope 3) do:
b-B/SEb graph with df & shading
tcdf LABELED
__OR__ calculator LinRegTTest
13
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Significance Test for Slope 4) conclude:
p vs. alpha
reject/fail to reject
convincing evidence?
14
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df=
n-2
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