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	1,000		45
2	750		55
3	1,500		200
4	1,250		100
5	1,250		145
6	750		20
7	1,500		445
8	1,000		65
9	2,000		455
10	1,000		45
11	1,100		55
12	1,650		345
13	300		20
14	2,250		435
15	1,750		345
16	2,000		435
17	1,500		225
18	2,000		545
19	500		30
20	400		30

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

1. 0.903

2. Reject H0 if t > 2.101

3. y = -168.440 + 0.291*x

4. 15

	r²	0.816
	r	0.903
	Std. Error	80.962
	n	20
	k	1
	Dep. Var.	Area
ANOVA table
Source	SS	df	MS	F	p-value
Regression	5,23,083.8895	1	5,23,083.8895	79.80	4.92E-08
Residual	1,17,986.1105	18	6,554.7839
Total	6,41,070.0000	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	-168.4395
Wattage	0.2911	0.0326	8.933	4.92E-08	0.2226	0.3596
Observation	Area	Predicted	Residual
1	45.0	122.7	-77.7
2	55.0	49.9	5.1
3	200.0	268.2	-68.2
4	100.0	195.4	-95.4
5	145.0	195.4	-50.4
6	20.0	49.9	-29.9
7	445.0	268.2	176.8
8	65.0	122.7	-57.7
9	455.0	413.8	41.2
10	45.0	122.7	-77.7
11	55.0	151.8	-96.8
12	345.0	311.9	33.1
13	20.0	-81.1	101.1
14	435.0	486.6	-51.6
15	345.0	341.0	4.0
16	435.0	413.8	21.2
17	225.0	268.2	-43.2
18	545.0	413.8	131.2
19	30.0	-22.9	52.9
20	30.0	-52.0	82.0