AP Statistics: Chapter 12.3

Condition #1

Random Sample Stated

Condition #2

n<10% of all [total population]

Condition #3

Scatterplot shows a clear linear trend

Condition #4

Residual plot shows random and equal scatter

Condition #5

Dot plot of residuals doesn’t show any major skewness or outliers

Test Statistic

t=b/SEb

df

n-2

Confidence Interval

b±t*SEb

Ho: B=0

There is no true linear relationship between x and y

Ha: B≠0

There is a linear relationship between x and y

Ha: B<0

There is a negative linear association between x and y

Ha: B>0

There is a positive linear association between x and y

Step 1 Parameter

Where B is the true slope relating [y in context] and [x in context]

Step 2

One Sample t-Test for Slope

Step 3

If Ho: B=0 is true,

P(b[sign]0)=P(t[sign][value])

Step 4 (Reject Ho)

There is evidence of a linear relationship between [y in context] and [x in context].

Step 4 (Fail to Reject Ho)

There is not evidence of a linear relationship between [y in context] and [x in context].

Calculation

Formula, Numbers in Formula, EST MOE, Interval, df

Confidence Interval Interpretation

We are [%] confident that the true slope relating [y in context] and [x in context] is between [value] and [value].

a (Bo) (y-intercept)

When [x in context] is 0, we predict [y in context] as a

b (B1) (slope)

For each 1 increase in [x in context], the predicted [y in context] increases/decreases by b

σ (s) (standard deviation)

The actual [y in context] typically varies by about s from the predicted [y in context]

Standard Error of the Slope Interpretation (SEb)

If we repeated the random sampling many times, the slope of the sample regression line would typically vary by about SEb from the slope of the true regression line for predicting the [y in context] from the [x in context]

Weak r

0-0.55

Moderately weak r

0.55-0.70

Moderately strong r

0.70-0.85

Strong r

0.85-1.0

r² interpretation

Approximately % of the variation in the predicted [y in context] is explained by the LSRL with [x in context]