AP Stat: Inferences about the Regression Model

LRSL

computed from a sample of ordered pairs; estimates the true linear relationship between the variables

y = a + bx is equivalent to….

s (standard deviation of residuals/ standard error of the line)

s = how the y’s vary about the line OR estimates the typical difference in actual & predicted

s formula

interpretation of standard error of the line

The difference in actual and predicted (y values) using this model, vary with a standard deviation of (WHATEVER S EQUALS)

Formula for CI of the slope

Why do we use the t distribution for Confidence interval of the slope?

LRSL is about the “mean” of the y’s (making z score inappropriate as it discusses one samp/prop.)

data graph with x and y

How to set up invT for confidence interval

How to interpret confidence intervals with LRSL

We can be (however many percents) confident that as acceptance rates (x) increases the graduation rates (y) decreases/increases by (CI interval)

OR

We can be (however many percents) confident that the true slope of the LRSL between x and y is between (CI interval)

Hypothesis test: hypotheses

CHECKS AND ASSUMPTIONS

Test statistic for hypothesis test

b - 0/SEb (standard error of the slope) = t (MUST SOLVE FOR SEb WHEN GIVEN “data”; bot in table of stats the calculator outputs

OK to proceed w/

Linear regression t test

WHAT CALC FUNCTION AM I USING FOR HYPOTHESIS TEST?

LinRegTTest

Interpretation for hypothesis tests

Since the p value is (), we reject Ho at that level (can state level or don’t). There is/isn’t enough evidence to conclude there is a relationship between x and y.

For confidence intervals, to state interval, what variable do we use to state

B

parameter for hypothesis tests

the true slope of the regression line between x and y

Positive or linear relationship with B

B>0 positive linear relationship

B<0 negative linear relationship

(NO LONGER TWO SIDED)

What does SEb tell us?

telling us how reliably we can estimate the true slope

What is needed for hypothesis test vs. ci

HT = t stat and solving (b-0/SEb = t) AS WELL AS P and interpretation

CI = solving for confidence interval/interpretation