- 1. Week 7 GM 533 Live Lecture B Heard(Do not post these, steal
them etc. without my permission. Students candownload a copy for
personal use)
2. Week 7 GM 533 THE HOSPITAL LABOR NEEDS CASE 14.6 Table 14.6
presents data concerning the need for laborin 16 U.S. Navy
hospitals. Here, y = monthly labor hoursrequired; x1 = monthly
X-ray exposures; x2 = monthlyoccupied bed days (a hospital has one
occupied bedday if one bed is occupied for an entire day); and x3
=average length of patients stay (in days). Figure 14.8gives the
Excel output of a regression analysis of thedata using the model.
Note that the variables x1, x2,and x3 are denoted as XRay, BedDays,
and LengthStayon the output. 3. Week 7 GM 533a) Find (on the
output) and report the values of b1, b2, and b3,the least squares
point estimates of 1, 2, and 3. Interpretb1, b2, and b3 .b)
Consider a questionable hospital for which XRay = 56,194,BedDays =
14,077.88, and LengthStay = 6.89. A pointprediction of the labor
hours corresponding to thiscombination of values of the independent
variables is givenon the Excel add-in output. Report this point
prediction andshow (within rounding) how it has been calculated.c)
If the actual number of labor hours used by thequestionable
hospital was y = 17,207.31, how does this yvalue compare with the
point prediction? 4. Week 7 GM 533a) b1 b2 b3For b1, As the x ray
exposures go up by 1, monthly labor hours go up by ______For b2 For
b3 5. Week 7 GM 533b) Just plug values into the equation = 1946.802
+ 0.3858x1 + 1.0394x2 - 413.7578x3c) How much less or greater was
the valuecalculated in part than 17207.31. That is allthey are
asking. 6. Week 7 GM 533 THE FRESH DETERGENT CASE 14.12 Model: y =
0 + 1 x1 + 2 x2 + 3 x3 + Samplesize: n = 30 7. Week 7 GM 5331
Report SSE, s2, and s as shown on the output. Calculate s2 from SSE
and othernumbers.2 Report the total variation, unexplained
variation, and explained variation as shownon the output.3 Report
R2 and (R Bar)2 as shown on the output. Interpret R2 and (R Bar) 2.
Show how(R Bar)2 has been calculated from R2 and other numbers.4
Calculate the F (model) statistic by using the explained variation,
the unexplainedvariation, and other relevant quantities. Find F
(model) on the output to checkyour answer (within rounding).5 Use
the F (model) statistic and the appropriate critical value to test
the significanceof the linear regression model under consideration
by setting equal to .05.6 Use the F (model) statistic and the
appropriate critical value to test the significanceof the linear
regression model under consideration by setting equal to .01.7 Find
the p-value related to F (model) on the output. Using the p-value,
test thesignificance of the linear regression model by setting =
.10, .05, .01, and .001.What do you conclude? 8. Week 7 GM 5331)
SSEs2sTo calculate s2 use the formula s2 = SSE/(n-(k+1)) where n is
the sample size (30)and k is 3. Take square root of s2 to get s. 9.
Week 7 GM 5332) Total variation, Unexplained variation, Explained
variation 10. Week 7 GM 5333) R2(R Bar)2Use equation and note if R2
and (R Bar)2 are close or not. 11. Week 7 GM 533 On part 4, use the
equation 12. Week 7 GM 533 On part 5, compareyour calculated
valueof F(model) from part4 to the F.05 valuefrom the table for
3and 26 degrees offreedom. If yourcalculated value isgreater than
the tablevalue, we would rejectH0: 1 = 2 = 3 = 0 13. Week 7 GM 533
On part 6, do just like you did part 5 exceptcompare your
calculated value of F(model)from part 4 to the F.01 value from the
table 14. Week 7 GM 533 Compare your p-value to alphas of 0.10,
0.05,0.01 and 0.001 and note what it means. Forexample if your
p-value was less than all ofthose alphas you would have very
strongevidence that your null hypothesis wasincorrect and very
strong evidence that atleast one of your x1, x2 or x3 is
significantlyrelated to y. 15. Week 7 GM 533 THE FUEL CONSUMPTION
CASE 14.16 Use the MINITAB output in Figure 14.9(a) todo (1)
through (6) for each of 0, 1, and 2 . 16. Week 7 GM 5331 Find bj,
sbj, and the t statistic for testing H0 : j = 0 on the output and
reporttheir values. Show how t has been calculated by using bj and
sbj .2 Using the t statistic and appropriate critical values, test
H0 : j = 0 versus Ha : 0 by setting a equal to .05. Which
independent variables are significantlyrelated to y in the model
with a = .05?3 Using the t statistic and appropriate critical
values, test H0 : j = 0 versus Ha :j 0 by setting equal to .01.
Which independent variables aresignificantly related to y in the
model with = .01?4 Find the p-value for testing H0 : j = 0 versus
Ha : j 0 on the output. Usingthe p-value, determine whether we can
reject H0 by setting a equal to.10, .05, .01, and .001. What do you
conclude about the significance of theindependent variables in the
model?5 Calculate the 95 percent confidence interval for j. Discuss
one practicalapplication of this interval.6 Calculate the 99
percent confidence interval for j . 17. Week 7 GM 533 I will get
you started on doing this for 0, youwill also need to do it for 1
and 2 . b0 sb0 t Where t = b0/sb0 This is part 1 18. Week 7 GM
533Part 2) We would reject H0: 0 = 0 (and concludethat the
intercept is significant) with = .05 if|t| > t.05/2 = t.025Since
t.025 = 2.571 (with n (k + 1) = 8 (2 + 1) =5 degrees of freedom),
we have t = 15.32 >t.025 = 2.571.We reject H0: 0 = 0 with = .05
and concludethat the intercept is significant at the .05 level. 19.
Week 7 GM 533 20. Week 7 GM 533 Part 3 is the same as the previous
one, but use= .01 . Remember t.01/2 = t.005(Use table value for
t.005) 21. Week 7 GM 533 Part 4 The Minitab output (given to us)
tells us thatthe p-value for testing H0: 0 = 0 is 0.000. Sinceit is
less than each given value of , we rejectH0: 0 = 0 at each of these
values of . We canconclude that the intercept 0 is significant
atthe .10, .05, .01, and .001 levels ofsignificance. 22. Week 7 GM
533 Part 5, use the formula for a 95% confidenceinterval for 0 23.
Week 7 GM 533 Part 6, use the formula for a 99% confidenceinterval
for 0 (similar to previous part) 24. Week 7 GM 533 Now you have to
go through ALL 6 parts againfor 1 and 2 . So this problem actually
has 18parts. 25. Week 7 GM 533THE REAL ESTATE SALES PRICE CASE
14.23The following MINITAB output relates to a househaving 2,000
square feet and a rating of 8. 26. Week 7 GM 533a Report (as shown
on the output) a point estimate of and a 95 percent confidence
interval for the mean sales price of all houses having 2,000 square
feet and a rating of 8.b Report (as shown on the output) a point
prediction of and a 95 percent prediction interval for the actual
sales price of an individual house having 2,000 square feet and a
rating of 8.c Find 99 percent confidence and prediction intervals
for the mean and actual sales prices referred to in parts a and b.
Hint: n = 10 and s = 3.24164. Optional technical note needed. 27.
Week 7 GM 533a) =remember this is in 1000s of dollarsThe 95% CI is
also given 28. Week 7 GM 533b) =remember this is in 1000s of
dollarsThe 95% PI is also given 29. Week 7 GM 533c) Find 99 percent
confidence and prediction intervals for the mean and actual sales
prices referred to in parts a and b. Hint: n = 10 and s = 3.24164.
So we know 30. Week 7 GM 533 So the previous chart gives us the
DistanceValue The 99% confidence interval for mean salesprice is
31. Week 7 GM 533We calculatedour DistanceValue and wewere given
s.You can now getthe lower andupper for the99% CI 32. Week 7 GM 533
For the 99% prediction interval, it would bevery similar but under
the square root younow have 1 + Distance Value
