Airfreight Breakage. A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. The data below, involving 10 shipments, were collected on the number of times the carton was transfered from one aircraft to another over the shipment route and the number of ampules found to be broken upon arrival. In short, x = the number of transfers and y = the number of broken ampules.
| Shipment | #1 |
#2 |
#3 |
#4 |
#5 |
#6 |
#7 |
#8 |
#9 |
#10 |
|---|---|---|---|---|---|---|---|---|---|---|
| x | 1 |
0 |
2 |
0 |
3 |
1 |
0 |
1 |
2 |
0 |
| y | 16 |
9 |
17 |
12 |
22 |
13 |
8 |
15 |
19 |
11 |
Use the TI84 to obtain the equation for the line that best fits the points (Least Squares Regression Line)
1. Report the regression equation (use appropriate notation).
2. What is the slope of this relationship (use appropriate notation)?
3. Interpret the slope in the context of the study.
4. What is the y-intercept of this relationship (use appropriate notation)?
5. Interpret the y-intercept in context of the study.
6. Report the coeffcient of correlation (use appropriate notation).
7. What does this coefficient of correlation tell you about the relationship?
8. Report the coefficient of determination (use appropriate notation)?
9. Interpret this coefficient of determination in context to the study.
10. Find the expected number of broken ampules when there is exactly one transfer in shipment. (show work)
11. Repeat this for 0, 2, and 3 number of transfers.
12. Does shipment number #3 (see data table) have an above or below average number of broken ampules as compared to others with the same number of transfers? Answer this with a sentence and justify your answer with a residual value.
13. Explain why a shipment with 0 transfers and 20 broken ampules is considered an outlier, while a shipment with 3 transfers and the same number of broken ampules would not be considered an outlier. When answering this question, make it clear that you understand what an outlier is in the regression sense.
An ANOVA test can be used to test whether a line is an appropriate representation of the relationship between two variables.
Here: Ho: There is not a linear relationship between (x) the number of transfers and (y) the number of broken ampules (versus) Ha: There is a linear relationship between the number of transfers and the number of broken ampules
The ANOVA Table is as follows:
Source |
df |
SS |
MS |
F |
Pvalue |
|---|---|---|---|---|---|
Regression |
1 |
SSR |
MSR = SSR/(1) |
MSR/MSE |
Fcdf(MSR/MSE,9999,df(reg),df(error)) |
Error |
n - 2 |
SSE |
MSE = SSE/(n-2) |
||
Total |
n - 1 |
SST |
Here:
SST is the sum of (y - ybar)^2 as described in the notes
SSE is the summ of (y - yhat)^2 as described in the notes. You might think of SSE as the sum of squared residuals.
SSR = SST - SSE
14. Make an ANOVA table filling in all the appropriate values (Show Work).
15. Make a conclusion based on your p-value.
(
The conclusion should be worded like step 5 of a 5-step hypothesis procedure)