(b) Find the correlation coefficient. (c-1) To test the correlation coefficient for significance at α = 0.1, fill in the followingNoodles & Company Sales Growth and Loyalty Card Sales (n = 74 restaurants) Annual Sales Growth (%)Loyalty Card % of Net Sales RestaurantGrowth%Loyalty%1-6.61.92-6.22.33-6.12.24-5.925-3.82.36-1.91.77-1.91.98-1.81.39-0.91.610-0.52.3110.41.9120.41.4130.62.3140.82.2150.821611.6171.81.31822.41940.7204.21.4214.32.4224.31.2234.42.5244.62.72551.5265.21.7275.31.5285.71.9295.82.53061.8316.42.2326.61.5336.62346.71.4356.82367.22377.32.3387.41.2397.51.7407.52417.51.4427.61.2437.61.9447.91.9458.11.7468.32.7478.70.7488.92498.91.3508.92.2519.21.75210.81.85310.91.55410.91.65511.22.55611.22.45711.41.35811.60.65911.92.46011.91.361131.56214.71.86314.826415.42.46515.81.36617.62.26717.70.56818.11.96918.31.67018.42.27121.41.77223.81.77324.20.67425.62

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 A1:B75. Mark Labels in First Row. Click OK. The output is, From the output, the correlation coefficient is -0.2014. Thus, the correlation coefficient is -0.2014.(c-1) The hypothesis is, Null hypothesis: H0:ρ=0 Alternative hypothesis: H1:ρ≠0 The test statistic is, t=rn-21-r2=-0.201474-21--0.20142=-0.2014×8.662789899=-1.7447 Thus, the test statistic is -1.7447. The degrees of freedom is, df=n-2=74-2=72 The hypothesis is two tailed test. The probability of t (1.7447) with 72 degrees of freedom can be obtained using the excel formula “=T.DIST.2T (1.7447, 72)”.The p-value is 0.0853. Decision rule: If p-value ≤ α, then reject the null hypothesis. Conclusion: The p-value (=0.0853) is less than the level of significance (=0.10). Based on decision rule, reject the null hypothesis. Thus, there is linear relationship between Sales Growth and Loyalty Card Sales at 10% level of significance.

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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Question

(b) Find the correlation coefficient.

(c-1) To test the correlation coefficient for significance at α = 0.1, fill in the following

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

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

Restaurant	Growth%	Loyalty%
1	-6.6	1.9
2	-6.2	2.3
3	-6.1	2.2
4	-5.9	2
5	-3.8	2.3
6	-1.9	1.7
7	-1.9	1.9
8	-1.8	1.3
9	-0.9	1.6
10	-0.5	2.3
11	0.4	1.9
12	0.4	1.4
13	0.6	2.3
14	0.8	2.2
15	0.8	2
16	1	1.6
17	1.8	1.3
18	2	2.4
19	4	0.7
20	4.2	1.4
21	4.3	2.4
22	4.3	1.2
23	4.4	2.5
24	4.6	2.7
25	5	1.5
26	5.2	1.7
27	5.3	1.5
28	5.7	1.9
29	5.8	2.5
30	6	1.8
31	6.4	2.2
32	6.6	1.5
33	6.6	2
34	6.7	1.4
35	6.8	2
36	7.2	2
37	7.3	2.3
38	7.4	1.2
39	7.5	1.7
40	7.5	2
41	7.5	1.4
42	7.6	1.2
43	7.6	1.9
44	7.9	1.9
45	8.1	1.7
46	8.3	2.7
47	8.7	0.7
48	8.9	2
49	8.9	1.3
50	8.9	2.2
51	9.2	1.7
52	10.8	1.8
53	10.9	1.5
54	10.9	1.6
55	11.2	2.5
56	11.2	2.4
57	11.4	1.3
58	11.6	0.6
59	11.9	2.4
60	11.9	1.3
61	13	1.5
62	14.7	1.8
63	14.8	2
64	15.4	2.4
65	15.8	1.3
66	17.6	2.2
67	17.7	0.5
68	18.1	1.9
69	18.3	1.6
70	18.4	2.2
71	21.4	1.7
72	23.8	1.7
73	24.2	0.6
74	25.6	2