Question

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Heater	Wattage		Area
1	1,500		183
2	1,000		30
3	1,500		345
4	1,500		235
5	1,500		465
6	2,000		565
7	1,500		455
8	1,250		455
9	1,000		255
10	1,750		545
11	1,750		480
12	450		20
13	2,200		725
14	350		15
15	200		15
16	300		15
17	1,750		475
18	1,300		445
19	800		20
20	300		35

Click here for the Excel Data File

1. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

2. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.10 significance level. (Negative value should be indicated by a minus sign. Round intermediate calculations and final answer to 3 decimal places.)

H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 1.3304

3. Develop the regression equation for effective heating based on wattage. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

4. Which heater looks like the “best buy” based on the size of the residual? (Negative value should be indicated by a minus sign. Round residual value to 2 decimal places.)

Answer 1

wattage	area																RESIDUAL OUTPUT
1500	183		Correlation
1000	30																Observation	Predicted Y	Residuals
1500	345			Column 1	Column 2		SUMMARY OUTPUT									1	393.357118	-210.357
1500	235		Column 1	1													2	222.115941	-192.116
1500	465		Column 2	0.901186	1		Regression Statistics									3	393.357118	-48.3571
2000	565						Multiple R	0.901186									4	393.357118	-158.357
1500	455						R Square	0.812137									5	393.357118	71.64288
1250	455						Adjusted R Square	0.8017									6	564.598295	0.401705
1000	255						Standard Error	103.8478									7	393.357118	61.64288
1750	545						Observations	20									8	307.736529	147.2635
1750	480																9	222.115941	32.88406
450	20						ANOVA										10	478.977706	66.02229
2200	725							df	SS	MS	F	Significance F					11	478.977706	1.022294
350	15						Regression	1	839181.1	839181.1	77.81455	5.93E-08					12	33.7506464	-13.7506
200	15						Residual	18	194118.7	10784.37							13	633.094766	91.90523
300	15						Total	19	1033300								14	-0.4975889	15.49759
1750	475																15	-51.869942	66.86994
1300	445							Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%		16	-17.621707	32.62171
800	20						Intercept	-120.366	51.88217	-2.32	0.032292	-229.367	-11.366	-229.367	-11.366		17	478.977706	-3.97771
300	35						X Variable 1	0.342482	0.038825	8.821255	5.93E-08	0.260915	0.42405	0.260915	0.42405		18	324.860647	120.1394
																	19	153.61947	-133.619