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		184
2	680		85
3	1,430		170
4	1,290		147
5	1,240		198
6	1,260		204
7	940		95
8	1,960		284
9	960		145
10	1,580		187
11	1,340		120
12	440		76
13	460		83
14	1,420		235
15	1,970		255
16	1,420		220
17	820		85
18	1,500		230
19	1,220		185
20	430		22

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

a)

correlation r='Sxy/(√Sxx*Syy) =

0.909

b)

test stat t=	r*(√(n-2)/(1-r2))=	9.227
P value    =	0.0000	(from excel:tdist(9.227,18,1)

since test statistic falls in rejection region we reject null hypothesis

c)

				sample size n=		20
				y̅ =		160.5000
				x̅ =		1193.0000
				Sxx=	Σ(Xi-X̅)2=	3935020.000
				Sxy      =	Σ(Xi-X̅)(Yi-Y̅)=	550890.000
				slope= β̂1 =	Sxy/Sxx=	0.14000
				intercept= β̂0 =	y̅-β1x̅=	-6.5161
				Least square line equation: ŷ = -6.516+0.140*x

d)

heater number 14 looks like the “best buy” based on the size of the residual

residual value =42.72 (since it has largest positive residual)