Question

The data below are the average monthly temperatures, in °F, and the monthly natural gas consumption, in ccf, for a household in northwestern Pennsylvania.

a.)Test the significance of the correlation coefficient using α = 0.05 and the claim ρ < 0. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision

b.) Find the equation of the regression line for the given data

	Temperature		47	35	21	27	39	48	61	65	70
	Consumption		34	169	248	134	137	100	19	34	12

Answer 1

( X)	( Y)	X^2	Y^2	X*Y
47	34	2209	1156	1598
35	169	1225	28561	5915
21	248	441	61504	5208
27	134	729	17956	3618
39	137	1521	18769	5343
48	100	2304	10000	4800
61	19	3721	361	1159
65	34	4225	1156	2210
70	12	4900	144	840

Line of Regression Y on X i.e Y = bo + b1 X
					X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
47	34	1.235	4167.425	-71.728
35	169	118.568	4962.413	-767.062
21	248	619.457	22333.629	-3719.507
27	134	356.791	1256.305	-669.506
39	137	47.457	1477.972	-264.84
48	100	4.457	2.086	3.049
61	19	228.345	6329.093	-1202.173
65	34	365.234	4167.425	-1233.729
70	12	581.345	7491.872	-2086.951