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 1,580 194

2 659 73

3 1,510 202

4 1,240 138

5 1,180 154

6 1,320 207

7 1,000 109

8 1,910 272

9    1,100 134

10 1,450   192

11 1,160 87

12 420 44

13 400 81

14 1,410 187

15 1,950 221

16 1,600 206

17 690 71

18 1,420 202

19 1,290 129

20 420 58

a. 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.)

The correlation of Wattage and Area is___________. The link (relationship) is_____________

b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.01 significance level. {Negative va!ue 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 > 2.5524

t = ________

Reject HO. It is quite reasonable to say the population correlation is positive

c. 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.)

The regression equation is: ________ =_________+________ __________

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

The 1st - 20th (which one) heater is the "best buy." It heats an area that is_________ square feet larger than estimated by the regression equation.

Answer 1

using minitab>stat>basic stat>correlation

we have

Correlation: heater wattage, area

Pearson correlation of heater wattage and area = 0.930
P-Value = 0.000

a.

The correlation of Wattage and Area is 0.930 .The link (relationship) is positive linear

b.

H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 2.5524

t = = 10.735

Reject HO. It is quite reasonable to say the population correlation is positive

using excel>data>data analysis>regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.930349
R Square	0.865549
Adjusted R Square	0.858079
Standard Error	24.42199
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	69113.14	69113.14	115.8773	2.84E-09
Residual	18	10735.81	596.4338
Total	19	79848.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-5.79517	15.29951	-0.37878	0.709281	-37.9383	26.34792	-37.9383	26.34792
heater wattage	0.129778	0.012056	10.76463	2.84E-09	0.104449	0.155106	0.104449	0.155106
RESIDUAL OUTPUT
Observation	Predicted area	Residuals
1	199.2539	-5.25386
2	79.72844	-6.72844
3	190.1694	11.83059
4	155.1294	-17.1294
5	147.3427	6.657289
6	165.5116	41.48839
7	123.9827	-14.9827
8	242.0805	29.91945
9	136.9605	-2.96048
10	182.3827	9.617267
11	144.7472	-57.7472
12	48.71154	-4.71154
13	46.11598	34.88402
14	177.1916	9.808381
15	247.2717	-26.2717
16	201.8494	4.150587
17	83.75156	-12.7516
18	178.4894	23.5106
19	161.6183	-32.6183
20	48.71154	9.288465

c.

The regression equation is: area =-5.795+0.130 * wattage

d.

The 9 th heater is the "best buy."

It heats an area that is136.96square feet larger than estimated by the regression equation.