The table below shows data collected on the vessel calls for a port in Ghana, from...

The table below shows data collected on the vessel calls for a port in Ghana, from 2007-2016 to study the relationship between the number of Commercial Vessels (C.V.) and Offshore Vessels (O. V.). Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 C. V. (X) 527 486 481 558 623 611 606 543 615 673 O. V. (Y ) 67 129 475 719 1175 1053 758 844 910 928 Assuming a linear regression model E(Y |X = x) = α + β(x − x¯): a. Fit a regression model of the number of offshore vessels on commercial vessels, and give practical interpretation of the regression parameter estimates. [10 Marks] b. Construct a 95% confidence and prediction intervals for the number of offshore vessels corresponding to 742 commercial vessels.

Solutions

Expert Solution

Create a table of all summations as below

n	Commerical Vessels (X)	Offshore Vessels (Y)	X^2	Y^2	XY
1	527	67	277729	4489	35309
2	486	129	236196	16641	62694
3	481	475	231361	225625	228475
4	558	719	311364	516961	401202
5	623	1175	388129	1380625	732025
6	611	1053	373321	1108809	643383
7	606	758	367236	574564	459348
8	543	844	294849	712336	458292
9	615	910	378225	828100	559650
10	673	928	452929	861184	624544
SUM →	5723	7058	3311339	6229334	4204922

Tabulate the values using regression parameters as below on excel

Regression Parameters	Commerical Vessels (X)	Offshore Vessels (Y)	Estimated Values	SSE
a	-1922.409	527	67	497.7659852	185559.334
b	4.59236236	486	129	309.4791286	32572.71586
		481	475	286.5173168	35525.72186
		558	719	640.1292183	6220.600207
		623	1175	938.6327715	55869.46671
		611	1053	883.5244232	28721.97113
		606	758	860.5626114	10519.08926
		543	844	571.2437829	74395.95394
		615	910	901.8938726	65.70930079
		673	928	1168.250889	57720.48983
				SUM →	487171.0521

orchestra answered 1 year ago

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