Question

A coffee company uses a​ data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that the coffee company needed to improve its​ package-sealing process, an experiment was conducted to determine the factors in the​ bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the​ bag-sealing equipment. Data were collected on 19 bags in which the plate gap was varied. Complete parts​ (a) through​ (e) below

Tear_Rating   Plate_Gap
0.08   -1.08
0.04   -0.68
0.35   0.27
0.88   0.25
0.32   -0.87
0.35   -0.98
0.61   -0.46
1.84   0.21
0.17   0.32
0.07   0.02
0.13   -1.19
3.99   0.58
0.02   0.19
0.63   0.21
0.04   -0.95
0.03   -0.28
0.35   -0.21
4.33   0.73
0.07   0.38

what is ?

b0=

b1=

Answer 1

The least square estimate of intercept and slope are,

From the data values,

	Tear_Rating, Y	Plate_Gap, X	X^2	Y^2	XY
	0.08	-1.08	1.1664	0.0064	-0.0864
	0.04	-0.68	0.4624	0.0016	-0.0272
	0.35	-0.27	0.0729	0.1225	-0.0945
	0.88	-0.25	0.0625	0.7744	-0.22
	0.32	-0.87	0.7569	0.1024	-0.2784
	0.35	-0.98	0.9604	0.1225	-0.343
	0.61	-0.46	0.2116	0.3721	-0.2806
	1.84	-0.21	0.0441	3.3856	-0.3864
	0.17	-0.32	0.1024	0.0289	-0.0544
	0.07	-0.02	0.0004	0.0049	-0.0014
	0.13	-1.19	1.4161	0.0169	-0.1547
	3.99	-0.58	0.3364	15.9201	-2.3142
	0.02	-0.19	0.0361	0.0004	-0.0038
	0.63	-0.21	0.0441	0.3969	-0.1323
	0.04	-0.95	0.9025	0.0016	-0.038
	0.03	-0.28	0.0784	0.0009	-0.0084
	0.35	-0.21	0.0441	0.1225	-0.0735
	4.33	-0.73	0.5329	18.7489	-3.1609
	0.07	-0.38	0.1444	0.0049	-0.0266
Sum	14.3	-9.86	7.375	40.1344	-7.6847