Question

Q13. The following table gives the lowest temperature (in degrees Celsius) on seven winter days and the number of emergency road service calls made to CAA on each of those days. Lowest temperature (x) -9 -17 -4 -23 -1 -123 Number of calls (y) 12 22 16 31 8 24 6 (a) Find the regression of the number of calls (y) on the lowest temperature (x). (b) To the nearest whole number, estimate the number of calls when the lowest temperature is -7°C. (c) Test to see if the regression is significant at a = 0.05.

Answer 1

a)

X	Y	X*Y	X*X	Y*Y
-9	12	-108	81	144
-17	22	-374	289	484
-4	16	-64	16	256
-23	31	-713	529	961
-1	8	-8	1	64
-12	24	-288	144	576
3	6	18	9	36

α = ΣΥ-ΣΧ? - ΣΧΣΧΥ ηΣ Χ2 – (ΣΧ)? - 119 - 1069 –-63.–1537 7. 1069 –-632 R 8.645

ΣΧ = -63, ΣΥ= 119, ΣΧ.Υ = -1537, ΣΧ? = 1069, ΣΥ? = 2521

6 = η-ΣΧΥ – ΣΧ.ΣΥ -ΣΧ2 – (Σ Χ)? - 7.–1537 ––63 - 119 7. 1069 – (-63)? R -0.928 η :

The regression equation is:

y = a + bir y = 8.645 - 0.928.2

B)

y = 8.645 -0.928x = 8.645 +0.928 +7 = 15.141

The number of calls is 15 calls at – 7°C temperature.

c)

η-ΣΧΥ – ΣΧ.ΣΥ * = [ΗΣΧ2 - (Σκ)- [n ΣΥ? - (ΣΥ)') r 7--1537 ––63 - 119 [7 - 1069 – –632] - [7 - 2521 – 119?] R -0.932

The hypothesis being tested is:

Ho : p= 0 HA: p=0

df = n – 2 = 7 – 2 = 5

The test statistic is:

t= t=r n - 2 1- p2 -0.932 7 – 2 1--0.9322 -5.75

The p-value is

p= Pr(|t5| > -5.75) = 0.0022

Since we have that p 0.0022 < 0.05, it is concluded that the null hypothesis H, is rejected.

Therefore, based on the sample correlation provided, it is concluded that there is enough evidence to claim that the population correlation p is different than 0, at the 0.05 significance level.