You will fully understand the confidence intervals and hypothesis tests after you have mastered Ch 10-Ch 13, but you can follow the patterns and use the tools for inference about the models you generated in Ch 3.
First, the confidence interval for the slope of the regression line is just a band around the estimate you created in Ch 3. You extend your interval t* standard deviations in each direction with your value of b as the center. The value of t* comes from the t-table using the confidence level C and df = n-2. Usually, the value of the standard deviation will be provided for you in the computer or calculator output.
The second tool is the hypothesis test. Look at the Minitab output on page 763. The values of b and SEb are given. The concept is that you are dividing the difference between the observed slope (b) and the default slope (0) by the standard deviation associated with the slope (Std dev of ddays) and call it the t-value. This is just like (x-mu)/sigma calculations for calculating z, except we have to use the t-table again. Find the probability (p) that we would get a t-value more extreme than the one we got and interpret. Remember how we found out how unlikely a z score of -2.08 was in problem 2.50? The interpretation is like that.
If p is small(usually anything less than .05), reject the null hypothesis. Therefore, the line through the data has a slope not equal to zero. Yippeeeee.
Subscribe to:
Post Comments (Atom)
Posts
3 comments:
I'm glad that you got that far so quickly. You're right--the standard error of b is not provided on the calculator. I don't know why.
If you have run the linear regression t-test, then you have the t-ratio or t-statistic. You also have have the value of b, don't you? Then solve t = b/SEb for SEb.
Note to the rest of the gang: Run the linear regression t-test FIRST.
The linear regression confidence interval (found on the TI-84 or by "hand") tells us a range of values that should be reasonable estimates for the true slope of the model - beta.
Was that fast enough?
If you have a TI-84 with the 2.30 operating system, it is the next to the last test (it follows LinRegTTest) under STAT.
If you don't have that operating system (and if it isn't showing up on your calculator then you don't have it), then you'll have to use the formula for confidence intervals from your text or your class notes.
Post a Comment