Question

1. FIND THE CORRELATION COEFFICIENT OF THE FOLLOWING DATA AND COMMENT ON ITS DIRECTION AND STRENGTH.HIGH TEMP(X)= 55 58 64 68 70 75 80 85 CANS SOLD(Y)= 340 335 410 450 460 610 735 7802.

2. IF THE EQUATION ABOVE IS A GOOD FIT PREDICT THE NUMBER OF CANS SOLD WHEN THE HIGH TEMP(X) IS 77.3.

3. FIND THE RESIDUALS FOR TEMP(X)= 58 and 70.4.

4. WHAT IS THE AMOUNT OF VARIATION IN CANS SOLD(Y) THAT KNOWING HIGH TEMP(X), EXPLAINS?

Answer 1

1.

Correlation Co-efficient for this data = 0.970

2.

	x	y	xy	x^2	Ycap	y-ycap
	55	340	18700	3025	283.0792128	56.92078717
	58	335	19430	3364	331.4800728	3.519927237
	64	410	26240	4096	428.2817926	-18.28179262
	68	450	30600	4624	492.8162725	-42.81627253
	70	460	32200	4900	525.0835125	-65.08351249
	75	610	45750	5625	605.7516124	4.24838763
	80	735	58800	6400	686.4197123	48.58028775
	85	780	66300	7225	767.0878121	12.91218786
Total	555	4120	298020	39259	4120	0

a	b
-604.2698859	16.13361998

Y = -604.27 + 16.13X

If X = 77.3, then Y = 642.86.

3. The Residuals for 70 is -65.08 and for 58 is 3.52

4. It explains 97% of variance as the correlation coefficient is 0.97