a). 8 students from the KCA University Financial Modelling class of January 2023 have been asked to generate the equation for the line of best fit from a data set obtained from a logistics company in which cargo handling cost is hypothesized to be influenced by the weight of cargo. They have presented their equations along with the total sum of squared errors/residuals (SSR) for the cargo handling cost (ksh) and the weight of cargo (tons) as follows;

Sno.	Student	Line of best fit	SSR
1.	Kendy	Y=18,600+140X	21,456
2.	Bernard	Y=16,200+164X	18,300
3.	Celine	Y=20,500+133X	31,240
4.	Newton	Y=21,200+125X	8,367
5.	Giovanna	Y=19,800+141X	14,520
6.	Elsie	Y=17,300+138X	8,674
7.	Beverly	Y=19,000+142X	12,496
8.	Nickson	Y=20,800+128X	8,582

Their lecturer has also generated the OLS estimate of the equation as Y= 20,600+128X.

Required:

Calculate the difference in the estimated cargo handling cost (based on the very best line of best fit) and the regression equation when the weight of cargo carried is 340 tons.

b). A local retail outlet has assembled sales data for two of its products that have elicited a lot of consumer excitement as follows;

Champagne (units)	45	48	43	49	55	54	59	63	65
Club soda (units)	14	18	17	23	18	26	24	25	27

Required:

Calculate the Spearmans Rank correlation coefficient.

c). 12 students from the KCA University Financial Modelling class of January 2023 have been asked to generate the equation for the line of best fit from a data set obtained from a rancher who fattens bulls using a certain animal feed supplement. They have presented their equations along with the total sum of squared errors/residuals (SSR) for the weight of the bulls (kgs) and the number of sachets of the feed supplement as follows;

Sno.	Student	Line of best fit	SSR
1.	Fatuma	Y=186+40X	212,456
2.	Brilliance	Y=162+64X	186,300
3.	Mercy	Y=205+33X	315,240
4.	Joseph	Y=212+25X	84,367
5.	Faith	Y=198+41X	147,520
6.	Everlyne	Y=173+38X	87,674
7.	Benedict	Y=190+42X	121,496
8.	Samuel	Y=208+28X	81,582
9.	Gregory	Y=199+37X	314,421
10.	Boaz	Y=206+24X	258,415
11.	Kennedy	Y=177+48X	154,783
12.	Harrison	Y=188+45X	94,752

Required:

Calculate the best estimate of the weight (in Kgs) of a bull that will be fed using 14 sachets of the feed supplement.