Deriving the regression equation, testing the model fit and obtains confidence interval for estimated values.
The Apex Corporation produces corrugated paper. It has collected monthly data from January 2001 through March 2003 on the following two variables:
y, total manufacturing cost per month (in thousands of dollars) (COST)
x, total machine hours used per month (MACHINE)
Data shown below: make any analysis necessary to answer the following questions:
1. What is the approximate regression equation relating y to x?
2. What percentage of the variation in y has been explained by the regression?
3. Are y and x linearly related? Conduct a hypothesis test to answer this question and use a 5% level of significance. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?
4. Apply the equation developed to estimate the average manufacturing cost in a month with 350 machine hours. Find a point estimate and a 95 percent confidence interval estimate. How reliable do you believe this forecast might be?
5. Employ the equation developed to estimate the average manufacturing cost in a month with 550 machine hours. Find a point estimate and a 95 percent confidence interval estimate. How reliable do you believe this forecast might be?
|
COST
|
MACHINE
|
|
1102
|
218
|
|
1008
|
199
|
|
1227
|
249
|
|
1395
|
277
|
|
1710
|
363
|
|
1881
|
399
|
|
1924
|
411
|
|
1246
|
248
|
|
1255
|
259
|
|
1314
|
266
|
|
1557
|
334
|
|
1887
|
401
|
|
1204
|
238
|
|
1211
|
246
|
|
1287
|
259
|
|
1451
|
286
|
|
1828
|
389
|
|
1903
|
404
|
|
1997
|
430
|
|
1363
|
271
|
|
1421
|
286
|
|
1543
|
317
|
|
1774
|
376
|
|
1929
|
415
|
|
1317
|
260
|
|
1302
|
255
|
|
1388
|
281
|