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		131
2	1,500		142
3	750		111
4	1,500		264
5	1,250		237
6	1,750		267
7	1,500		61
8	2,000		135
9	2,000		263
10	2,000		263
11	750		125
12	1,500		76
13	2,000		77
14	750		170
15	1,000		165
16	1,000		152
17	1,000		238
18	1,750		209
19	1,250		167
20	1,750		75

1. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Round your answer to 4 decimal places.)

2. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.010 significance level. (Round intermediate calculations and final answer to 3 decimal places.)

H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 2.552

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? (Round residual value to 3 decimal places.)

Answer 1

1)

correlation r='Sxy/(√Sxx*Syy) =

0.1256

direct relationship

b)

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ>		0

Decision rule: reject Ho if test statistic t>2.552

test stat t=

r*(√(n-2)/(1-r2))=

0.537

P value    =

0.2988

(from excel:tdist(0.5373,18,1)

Fail to reject the null hypothesis

c)

sample size n=	20
x̅ =	1425.0000
y̅ =	166.4000
Sxx=	Σ(Xi-X̅)2=	3637500.000
Sxy      =	Σ(Xi-X̅)(Yi-Y̅)=	73350.000
slope= β̂1 =	Sxy/Sxx=	0.0202
intercept= β̂0 =	y̅-β1x̅=	137.6649
Least square line equation: ŷ =137.665+0.020*x

heater 4 is appear to be best buy since provide highest positive residual of 96.088