(b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)(c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round tcalc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.)tcalc=p-value=Noodles & Company Sales Growth and Loyalty Card Sales (n = 74 restaurants) Annual Sales Growth (%)Loyalty Card % of Net Sales RestaurantGrowth%Loyalty%1-8.32.12-4.02.53-3.91.74-3.42.15-3.32.56-1.93.07-0.82.38-0.42.39-0.22.210-0.22.3110.52.1120.62.5130.82.0141.92.0152.02.0162.12.6172.82.2182.92.1194.01.9204.02.2214.00.7224.02.0234.21.8244.62.1255.12.5265.12.6275.52.0285.92.0295.91.4306.02.0316.12.1326.12.1336.12.7346.32.0356.62.0366.91.6376.91.9387.11.6397.41.8407.72.2417.92.2428.12.8438.32.4448.53.1458.62.2468.71.3478.81.8488.82.5498.91.9509.12.0519.52.45210.22.25310.72.25411.00.35511.31.95611.41.95711.52.25811.72.65911.82.26011.92.16112.52.06212.80.96313.81.16414.13.46514.21.26614.62.16714.90.96815.42.26916.21.77017.22.47118.42.87220.81.17325.50.67428.81.8

The data shows the Noodles & Company Sales Growth and Loyalty Card Sales for 74 restaurants.(b) The correlation value is obtained by using EXCEL procedure as follows: Enter the data. Select Data > Data Analysis >Correlation> OK. Enter Input Range as B1:C74. Mark Labels in First Row. Click OK. The output is, From the output, the correlation coefficient is -0.294.(c-1) The test statistic is, tcalc=rn-21-r2=-0.29474-21--0.2942=-0.2948.87762425=-2.610 Thus, the tcalc value is -2.610. The degrees of freedom is, df=n-2=74-2=72 The hypothesis is two tailed test. The probability of t (2.610) with 72 degrees of freedom can be obtained using the excel formula “=T.DIST.2T (2.610, 72)”.The p-value is 0.0110. Thus, the p-value is 0.0110.

Answered: (b) Find the correlation coefficient.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

(b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

(c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round t_calc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.)

tcalc=

p-value=

Noodles & Company Sales Growth and Loyalty Card Sales (n = 74 restaurants)

	Annual Sales Growth (%)	Loyalty Card % of Net Sales

Restaurant	Growth%	Loyalty%
1	-8.3	2.1
2	-4.0	2.5
3	-3.9	1.7
4	-3.4	2.1
5	-3.3	2.5
6	-1.9	3.0
7	-0.8	2.3
8	-0.4	2.3
9	-0.2	2.2
10	-0.2	2.3
11	0.5	2.1
12	0.6	2.5
13	0.8	2.0
14	1.9	2.0
15	2.0	2.0
16	2.1	2.6
17	2.8	2.2
18	2.9	2.1
19	4.0	1.9
20	4.0	2.2
21	4.0	0.7
22	4.0	2.0
23	4.2	1.8
24	4.6	2.1
25	5.1	2.5
26	5.1	2.6
27	5.5	2.0
28	5.9	2.0
29	5.9	1.4
30	6.0	2.0
31	6.1	2.1
32	6.1	2.1
33	6.1	2.7
34	6.3	2.0
35	6.6	2.0
36	6.9	1.6
37	6.9	1.9
38	7.1	1.6
39	7.4	1.8
40	7.7	2.2
41	7.9	2.2
42	8.1	2.8
43	8.3	2.4
44	8.5	3.1
45	8.6	2.2
46	8.7	1.3
47	8.8	1.8
48	8.8	2.5
49	8.9	1.9
50	9.1	2.0
51	9.5	2.4
52	10.2	2.2
53	10.7	2.2
54	11.0	0.3
55	11.3	1.9
56	11.4	1.9
57	11.5	2.2
58	11.7	2.6
59	11.8	2.2
60	11.9	2.1
61	12.5	2.0
62	12.8	0.9
63	13.8	1.1
64	14.1	3.4
65	14.2	1.2
66	14.6	2.1
67	14.9	0.9
68	15.4	2.2
69	16.2	1.7
70	17.2	2.4
71	18.4	2.8
72	20.8	1.1
73	25.5	0.6
74	28.8	1.8