Question

Annual Sales Growth (%) and Loyalty Card Usage (% of Net Sales) (n - 74 restaurants) Store Growth% Loyalty% Store 38 39 Growth% Loyalty% 1.6 2.5 3.9 7.7 7.9 2.2 2.8 3.3 1.9 0.8 0.4 0.2 0.2 2.5 3.0 2.3 2.3 2.2 43 45 47 8.5 8.6 2.2 1.8 1.9 2.1 2.5 2.0 2.0 2.0 2.6 2.2 8.8 8.8 8.9 9.1 9.5 10.2 10.7 11.0 0.6 0.8 1.9 49 50 51 52 53 2.0 2.2 2.2 2.8 4.0 4.0 4.0 1.9 2.2 0.7 2.0 11.4 11.5 11.7 11.8 11.9 12.5 12.8 13.8 14.1 14.2 14.6 14.9 15.4 16.2 17.2 18.4 20.8 25.5 28.8 1.9 20 2.6 59 60 61 62 63 23 24 25 26 27 28 29 30 4.2 2.0 0.9 2.5 2.0 2.0 5.5 65 5.9 6.0 6.1 6.1 6.1 2.0 2.1 0.9 2.2 69 70 71 72 73 74 32 34 35 2.7 2.0 2.0 6.6 6.9 6.9 0.6 37

Answer 1

B)

X	Y	X^2	Y^2	Xy
-8.3000	2.100	69	4	-17
-4.0000	2.500	16	6	-10
-3.9000	1.700	15	3	-7
-3.4000	2.100	12	4	-7
-3.3000	2.500	11	6	-8
-1.9000	3.000	4	9	-6
-0.8000	2.300	1	5	-2
-0.4000	2.300	0	5	-1
-0.2000	2.200	0	5	0
-0.2000	2.300	0	5	0
0.5000	2.100	0	4	1
0.6000	2.500	0	6	2
0.8000	2.000	1	4	2
1.9000	2.000	4	4	4
2.0000	2.000	4	4	4
2.1000	2.600	4	7	5
2.8000	2.200	8	5	6
2.9000	2.100	8	4	6
4.0000	1.900	16	4	8
4.0000	2.200	16	5	9
4.0000	0.700	16	0	3
4.0000	2.000	16	4	8
4.2000	1.800	18	3	8
4.6000	2.100	21	4	10
5.1000	2.500	26	6	13
5.1000	2.600	26	7	13
5.5000	2.000	30	4	11
5.9000	2.000	35	4	12
5.9000	1.400	35	2	8
6.0000	2.000	36	4	12
6.1000	2.100	37	4	13
6.1000	2.100	37	4	13
6.1000	2.700	37	7	16
6.3000	2.000	40	4	13
6.6000	2.000	44	4	13
6.9000	1.600	48	3	11
6.9000	1.900	48	4	13
7.1000	1.600	50	3	11
7.4	1.800	55	3	13
7.7	2.200	59	5	17
7.9000	2.200	62	5	17
8.1000	2.800	66	8	23
8.3000	2.400	69	6	20
8.5000	3.100	72	10	26
8.6000	2.200	74	5	19
8.7000	1.300	76	2	11
8.8000	1.800	77	3	16
8.8000	2.500	77	6	22
8.9000	1.900	79	4	17
9.1000	2.000	83	4	18
9.5000	2.400	90	6	23
10.2000	2.200	104	5	22
10.7000	2.200	114	5	24
11.0000	0.300	121	0	3
11.3000	1.900	128	4	21
11.4000	1.900	130	4	22
11.5000	2.200	132	5	25
11.7000	2.600	137	7	30
11.8000	2.200	139	5	26
11.9000	2.100	142	4	25
12.5000	2.000	156	4	25
12.8000	0.900	164	1	12
13.8000	1.100	190	1	15
14.1000	3.400	199	12	48
14.2000	1.200	202	1	17
14.6000	2.100	213	4	31
14.9000	0.900	222	1	13
15.4000	2.200	237	5	34
16.2000	1.700	262	3	28
17.2000	2.400	296	6	41
18.4000	2.800	339	8	52
20.8000	1.100	433	1	23
25.5000	0.600	650	0	15
28.8000	1.800	829	3	52

Sum x	Sum y	Sum x^2	Sum y^2	Sum xy	N
548.6000	150.1000	7267.4200	326.7300	372.4000	48.0000

Corr coef, r =
{n*sum(XY)-sum(X)*sum(Y)}/{ sqrt(n*sum(x^2)-[sum(x)]^2) * sqrt(n*sum(y^2)-[sum(y)]^2) }
{48*372.4-548.6*150.1}/{ sqrt(48*7267.42-[548.6]^2) * sqrt(48*326.73-[150.1]^2) }
-0.280

C1)

R=-0.280
n= 48.0000

t = r*sqrt((n-2)/(1-r^2))
-0.280187418969879*SQRT((48-2)/(1--0.280187418969879^2))
-1.980

p-value
2*(1-P(T<|t|)
2*(1-P(T<abs(-1.9796164430854))
T.DIST.2T(abs(-1.9796164430854),48-2)
0.0537

C2)

Ho: the correlation Coefficient is not significant. H1: in the correlation Coefficient is significant.

Since the value is greater than 5%, the null hypothesis is not rejected at 5% level of significance.

Hence, I conclude that the correlation Coefficient is not significant