Question

C -- Given the following ANOVA table:

Source	DF				SS				MS				F
Regression		1				1,200.0				1,200.00				24.00
Error		12				600.0				50.00
Total		13				1,800.0

1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

2. Assuming a direct relationship between the variables, what is the correlation coefficient? (Round your answer to 2 decimal places.)

3. Determine the standard error of estimate. (Round your answer to 2 decimal places.)

D -- 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		290
2	750		292
3	1,500		148
4	1,250		246
5	1,250		203
6	750		85
7	1,250		237
8	1,000		139
9	1,500		64
10	1,000		171
11	1,750		163
12	1,250		175
13	750		264
14	1,500		50
15	1,750		163
16	1,500		177
17	1,250		118
18	1,750		122
19	1,000		144
20	1,500		103

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 0.025 significance level. (Round intermediate calculations and final answer to 3 decimal places.)

H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 2.101

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

C.

a) the coefficient of determination R² = SS_Regression/SS_total = 1200/1800 = 0.667

b) correlation coefficient = sqrt( R²) = 0.82 ( given it is a direct relationship)

c) standard error of estimate = Sqrt(SSE/N-2) = Sqrt(600/12) = 7.071

D) Excel results

a) Correlation coefficient = -0.4294, there is an indirect relationship .

b) H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 2.101

test statistic t = = -2.015

Fail to reject null hypothesis and conclude that there is no significant evidence that correlation coefficient is greater than zero.

c)

Regression Statistics
Multiple R	0.42935
R Square	0.184341
Adjusted R Square	0.139027
Standard Error	65.27225
Observations	20

ANOVA
	df	SS	MS	F	Significance F
Regression	1	17331.79	17331.79	4.068049	0.058869
Residual	18	76688.41	4260.467
Total	19	94020.2

	Coefficients	Standard Error	t Stat	P-value
Intercept	283.5205	59.24965	4.785184	0.000148
Wattage	-0.09174	0.045484	-2.01694	0.058869

equation is

Heating Area = 283.521 - 0.092* Wattage

d) RESIDUAL OUTPUT

Observation	Predicted Area	Residuals
1	191.7815	98.21851
2	214.7162	77.28376
3	145.912	2.088012
4	168.8467	77.15326
5	168.8467	34.15326
6	214.7162	-129.716
7	168.8467	68.15326
8	191.7815	-52.7815
9	145.912	-81.912
10	191.7815	-20.7815
11	122.9772	40.02276
12	168.8467	6.153263
13	214.7162	49.28376
14	145.912	-95.912
15	122.9772	40.02276
16	145.912	31.08801
17	168.8467	-50.8467
18	122.9772	-0.97724
19	191.7815	-47.7815
20	145.912	-42.912

based on the residuals the best buy is heater 18 with 1750 watts because its residual is close to zero.