Unit 9- Slopes

What is the population regression model?

-µy = a + βx

Constructing a Confidence Interval

What are the conditions for β?

1). The true relationship between x and y has to be linear

2). The SD of y does not vary with x

3). For a particular x-value, the responses (y-values) have to be approximately normally distributed

What procedure allows you to find the slope of a population regression line?

T interval for the slope

How do you find the df for confidence intervals of a population regression line?

df = n-2

       Ex: 25-2=23 degrees of freedom

Confidence interval for a slope of a regression line-

β ± (test statistic t)(standard error of β)

Performing a Significance Test

State null and alternative hypothesis

Define parameters

Identify Procedure

Check Conditions

Solve for test statistic and p-value

Draw Conclusion

Null Hypothesis: claim of no difference, no change, or no relationship

Ho: β=0

Ha: β>0 or β<0 or β≠0

linear positive relationship = β>0

linear negative relationship = β<0

test of a linear relationship = β ≠ 0

How do you calculate test statistic t for a slope?

t= (β-βo) divided by Se of β

β0 → slope used in null (often 0)