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The Apex corporation produces corrugated paper. It has collected monthly data from January 2001 through March...

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)

The data are shown below.

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

Answer the following question

Fill in the blanks for the following statement: “I am 95% confident that the average manufacturing cost at the Apex corporation for all months with 350 total machine hours is between ____ and ____.”

please show me steps

Solutions

Expert Solution

This problem can be solved using regression.

Following are the steps

1	calculate regression coefficient using mentioned formula
2	calculate yhat using regression formula
3	calculate root mean square error(syx)
4	calculate standard error for prediction
5	calculate t critical
6	calculate lower and upper value of interval

Step 1.

y = a+bx

To calculate a and b

y	x	xy	x^2	y^2
1102	218	240236	47524	1214404
1008	199	200592	39601	1016064
1227	249	305523	62001	1505529
1395	277	386415	76729	1946025
1710	363	620730	131769	2924100
1881	399	750519	159201	3538161
1924	411	790764	168921	3701776
1246	248	309008	61504	1552516
1255	259	325045	67081	1575025
1314	266	349524	70756	1726596
1557	334	520038	111556	2424249
1887	401	756687	160801	3560769
1204	238	286552	56644	1449616
1211	246	297906	60516	1466521
1287	259	333333	67081	1656369
1451	286	414986	81796	2105401
1828	389	711092	151321	3341584
1903	404	768812	163216	3621409
1997	430	858710	184900	3988009
1363	271	369373	73441	1857769
1421	286	406406	81796	2019241
1543	317	489131	100489	2380849
1774	376	667024	141376	3147076
1929	415	800535	172225	3721041
1317	260	342420	67600	1734489
1302	255	332010	65025	1695204
1388	281	390028	78961	1926544

sum(y) =40424,sum(x^2) = 2703831, sum(x) = 8337, sum(x*y) = 13023399

a = 206.8651,b = 4.178798

regression equation : y = 206.8651+4.178798*x

Step2

Calculate yhat for x0= 350

= 206.8651+4.178798*350 = 1669.445

Step3

Calculate RMSE

residual = yhat - y where yhat is calculated by putting value of x in above formula

yhat	residual	residual^2
1117.843	-15.8432	251.0057
1038.446	-30.446	926.9583
1247.386	-20.3859	415.5852
1364.392	30.60774	936.8337
1723.769	-13.7689	189.5831
1874.206	6.794342	46.16309
1924.351	-0.35124	0.123368
1243.207	2.792892	7.800245
1289.174	-34.1739	1167.855
1318.425	-4.42548	19.58486
1602.584	-45.5838	2077.88
1882.563	4.436745	19.68471
1201.419	2.580875	6.660917
1234.85	-23.8495	568.7992
1289.174	-2.17389	4.725797
1402.001	48.99855	2400.858
1832.418	-4.41767	19.51585
1895.1	7.90035	62.41554
2003.748	-6.74841	45.54099
1339.319	23.68053	560.7675
1402.001	18.99855	360.9451
1531.544	11.45581	131.2355
1778.093	-4.0933	16.75507
1941.066	-12.0664	145.5988
1293.353	23.64731	559.1954
1272.459	29.5413	872.6886
1381.107	6.892547	47.5072

Syx = 21.78281

Step4:

calculate standard error for prediction

= 4.227521

here n= 27

step5:

calculate t critical = t table at 0.05 and degrees of freedom = n-2 = 27-2=25

t critical = 2.059539

Step 6:

calculate confidence interval

lower = 1660.738

upper = 1678.151

therefore

milcah answered 7 months ago

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