Annual Sales Growth (%) and Loyalty Card Usage (% of Net Sales) (n - 74 restaura

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

Explanation / Answer

B)

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

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

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