An article gave the data, shown in the table below, on dimensions of 27 representative food products. Product Material Height Maximum Width Minimum Width Elongation Volume 1 glass 7.7 2.50 1.80 1.50 121 2 glass 6.2 2.90 2.70 1.07 139 3 glass 8.5 2.15 2.00 1.98 178 4 glass 10.4 2.90 2.60 1.79 288 5 plastic 8.0 3.20 3.15 1.25 328 6 glass 8.7 2.00 1.80 2.17 94 7 glass 10.2 1.60 1.50 3.19 115 8 plastic 10.5 4.80 3.80 1.09 517 9 plastic 3.4 5.90 5.00 0.29 332 10 plastic 6.9 5.80 4.75 0.59 567 11 tin 10.9 2.90 2.80 1.88 340 12 plastic 9.7 2.45 2.10 1.98 177 13 glass 10.1 2.60 2.20 1.94 236 14 glass 13.0 2.60 2.60 2.50 237 15 glass 13.0 2.70 2.60 2.41 358 16 glass 11.0 3.10 2.90 1.77 314 17 cardboard 8.7 5.10 5.10 0.85 635 18 cardboard 17.1 10.20 10.20 0.84 1250 19 glass 16.5 3.50 3.50 2.36 651 20 glass 16.5 2.70 1.20 3.06 300 21 glass 9.7 3.00 1.70 1.62 312 22 glass 17.8 2.70 1.75 3.30 303 23 glass 14.0 2.50 1.70 2.80 247 24 glass 13.6 2.40 1.20 2.83 196 25 plastic 27.9 4.40 1.20 3.17 1203 26 tin 19.5 7.50 7.50 1.30 2326 27 tin 13.8 4.25 4.25 1.62 730 (a) Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score. (Round your numerical values to two decimal places. Use x1 for minimum width, x2 for the maximum width and x3 for the elongation score.) y = Calculate the test statistic and the P-value . (Round your answer to two decimal places.) F = P=

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 27PFA

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Question

An article gave the data, shown in the table below, on dimensions of 27 representative food products.

Product	Material	Height	Maximum Width	Minimum Width	Elongation	Volume
1	glass	7.7	2.50	1.80	1.50	121
2	glass	6.2	2.90	2.70	1.07	139
3	glass	8.5	2.15	2.00	1.98	178
4	glass	10.4	2.90	2.60	1.79	288
5	plastic	8.0	3.20	3.15	1.25	328
6	glass	8.7	2.00	1.80	2.17	94
7	glass	10.2	1.60	1.50	3.19	115
8	plastic	10.5	4.80	3.80	1.09	517
9	plastic	3.4	5.90	5.00	0.29	332
10	plastic	6.9	5.80	4.75	0.59	567
11	tin	10.9	2.90	2.80	1.88	340
12	plastic	9.7	2.45	2.10	1.98	177
13	glass	10.1	2.60	2.20	1.94	236
14	glass	13.0	2.60	2.60	2.50	237
15	glass	13.0	2.70	2.60	2.41	358
16	glass	11.0	3.10	2.90	1.77	314
17	cardboard	8.7	5.10	5.10	0.85	635
18	cardboard	17.1	10.20	10.20	0.84	1250
19	glass	16.5	3.50	3.50	2.36	651
20	glass	16.5	2.70	1.20	3.06	300
21	glass	9.7	3.00	1.70	1.62	312
22	glass	17.8	2.70	1.75	3.30	303
23	glass	14.0	2.50	1.70	2.80	247
24	glass	13.6	2.40	1.20	2.83	196
25	plastic	27.9	4.40	1.20	3.17	1203
26	tin	19.5	7.50	7.50	1.30	2326
27	tin	13.8	4.25	4.25	1.62	730

(a)

Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score. (Round your numerical values to two decimal places. Use x₁ for minimum width, x₂ for the maximum width and x₃ for the elongation score.)

y =

Calculate the test statistic and the P-value . (Round your answer to two decimal places.)

F =

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