Q1. We search for a possible relationship between the amount of sales and the si

Question

Q1. We search for a possible relationship between the amount of sales and the size of the shop of the following form: We have the following data Observation 1 2 3 4 5 67 89 10 11 1213 14 Meter Sq(x) 1.7 1.6 2.8 5.6 1.3 2.2 1.3 1.1 3.2 1.5 5.2 4.6 5.8 3 Sales (y)3.7 3.9 6.7 9.5 3.4 5.6 3.7 2.7 5.5 2.9 10.7 7.6 11.8 4.1 1. Find the following quantities: bo.bi SSE, s, Sbo So 2. Make the tests Ho: 0 and Ho: B10. 3. want to open a new shop which has a size of 5-m2. What is the average number of sales? 4. What can you say about the average sales for 5m2? 5. What can you say about the sales for a single 5 m2 shop?

Explanation / Answer

1)

b0 = 0.9645 ,
b1 = 1.6699
SSE = 11.2066
s = 0.9664
s_b0 = 0.5262
s_b1 = 0.1569

2)

for Ho: b0 = 0
p-value = 0.09172 > 0.05 ,
b0 is not significant

Ho:b1 = 0
p-value = 1.82269*10^(-7) < 0.05
b1 is significant

3)
y^ = a+ b *x
= 0.9645 + 1.6699*x
= 0.9645 + 1.6699* 5
= 9.314

SUMMARY OUTPUT Regression Statistics Multiple R 0.950883275 R Square 0.904179003 Adjusted R Square 0.89619392 Standard Error 0.966379679 Observations 14 ANOVA df SS MS F Significance F Regression 1 105.7476095 105.7476095 113.2335128 1.82269E-07 Residual 12 11.20667621 0.933889684 Total 13 116.9542857 Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.964473659 0.526193302 1.832926522 0.091726832 -0.182003058 x 1.669862317 0.156925375 10.64112366 1.82269E-07 1.327951298

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