Question

Energy Consumption The annual energy consumption in billions of Btu for both natura; gas and coal is shown for random selection os states

Gas 223 474 377 289 747 146

Coal 478 631 413 356 736 474

Find the amount of coal used when 500 Btu of natural gas is used

Answer 1

Here we have to find the regression relation

	gas	Coal	x^2	xy	y^2
	223	478	49729	106594	228484
	474	631	224676	299094	398161
	377	413	142129	155701	170569
	289	356	83521	102884	126736
	747	736	558009	549792	541696
	146	474	21316	69204	224676
Sum	2256	3088	1079380	1283269	1690322

y^ = a + bx Here if the regresssion equation is

a = [(Σy) (Σx² ) - (Σx) (Σxy)]/ [ n (Σx²) - (Σx)² ]

a = [3088 * 1079380 - 2256 * 1283269]/ [6 * 1079380 - 2256²]

a = 315.8987

b =  [ n(Σxy) - (Σx)((Σy)]/ [ n (Σx² ) - (Σx)² ]

b = [6 * 1283269 - 2256 * 3088]/[ 6 * 1079380 - 2256²]

b = 0.5286

y^ = 0.5286x + 315.8987

Here

x = 500 Btu

y^ = 0.5286 * 500 + 315.8987 = 580.2178