Question

Using excel compute correlation coefficients, correlation matrix and test the significance of the correlation coefficients between sales with price,  sales with advertisments using alpha 0.05

Sales	Price	Adver
19.98	14.10	15.19
19.98	18.65	15.19
19.98	18.65	13.87
19.98	18.65	12.83
19.98	18.65	13.16
19.98	18.65	15.19
19.98	18.65	13.92
20.10	18.73	14.42
20.12	18.75	13.83
20.13	18.75	14.50
20.14	18.75	13.87
20.12	18.75	13.64
20.12	13.87	14.31
20.13	14.27	13.85
20.14	18.76	14.20
20.14	18.77	13.64
20.13	13.87	14.33
20.13	14.14	13.14
20.13	18.76	13.81
20.13	18.72	15.19
20.13	18.76	13.13
19.18	18.76	13.63
14.78	18.74	15.19
16.04	18.75	13.89
20.12	18.75	14.28
19.75	18.75	15.19
19.65	18.75	13.12
19.69	13.79	13.78
20.12	13.49	15.19
20.12	14.89	15.19
20.13	13.94	15.19
20.14	13.67	15.19
15.14	14.43	15.19
14.33	18.75	15.19
16.24	18.22	13.14
19.93	14.06	13.45
21.06	14.43	13.00
21.19	19.48	13.60
21.23	15.15	14.46
20.12	13.79	14.94
14.73	14.31	15.19
14.57	19.50	15.19
15.94	13.85	15.19
20.70	14.23	13.43
19.57	19.31	14.37
19.60	19.29	15.19
19.94	13.76	15.19
21.28	13.45	15.19
14.56	15.13	15.19
14.39	19.43	15.19
16.81	13.26	15.19
19.86	13.92	15.19

  

Answer 1

From the given data

1 see ecv aid SPA 34.1 3810 40 4 4 4 3 FA 19 19 19 2 20 20 - 234 5 6 7 891 11 2 3 4 5 6 7 8 9 20 21 0

The correlation coefficient matrix is

	Sales	Price	Adver
Sales	1
Price	-0.0836	1
Adver	-0.36354	-0.25148	1

i)

H0: There is no correlation between Sales and Price

H1: There exist correlation between Sales and Price

Let the los be alpha = 5%

The sample size is n 52, so then the number of degrees of freedom is df-n-2-52-2-50 The corresponding critical correlation value re for a significance level of a 0.05, for a two-tailed た= 0.273 Observe that in this case, the null hypothesis is rejected ifr> re 0.273.

Here correlation between Price and Sale is -0.0836 i.e. |r_xy| = 0.0836 which is < r_c. so we accept H0

Thus we conclude that there is no correlation between Sales and Price

ii)

H0: There is no correlation between Sales and Advert

H1: There exist correlation between Sales and Advert

Let the los be alpha = 5%

Here correlation between Price and Advert is -0.36354 i.e. |r_xy| = 0.36354 which is > r_c. so we do not accept H0

Thus we conclude that there exist correlation between Sales and Advert

iii)  

H0: There is no correlation between Price and Advert

H1: There exist correlation between Price and Advert

Let the los be alpha = 5%

Here correlation between Price and Advert is -0.25148 i.e. |r_xy| = 0.25148 which is > r_c. so we do not accept H0

Thus we conclude that there exist correlation between price and Advert.