9.1-9.3

population

population

Muy=alpha+Bx

sample

y-hat=a+bx

sampling distribution of b

unimodal curve

N(0, sigma*b → sigmaSEb)

statstic

y-int a

slope b

SD of residuals S

SD of slope SEb

parameter

y-int alpha

slope B

SD of residuals sigma

SD of slope sigma b

Confidence Intervals for Slope 1) state:

parameter: true slope of the population

LSRL for x context vs. y context

statistic = b

confidence level

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

Confidence Intervals for Slope 3) do:

By Hand

b+-t*SEb

t* = invT (tail %, df (n-2) use positive slope

OR LinRegTInt

Confidence Intervals for Slope 4) conclude:

We are % confident that the interval (,) captures the true slope of x-int v. y-int.

Significance Test for Slope 1) state:

parameter in context

H0, Ha

alpha

Significance Test for Slope 2) plan:

1 sample t-test (for slope)

LINER

Significance Test for Slope 3) do:

b-B/SEb graph with df & shading

tcdf LABELED

OR calculator LinRegTTest

Significance Test for Slope 4) conclude:

p vs. alpha

reject/fail to reject

convincing evidence?

df=

n-2