Question

Please use minitab

The air flow through a value on an automotive air pollution control device is believed to be controlled by three discrete factors; Arm Length, Spring Load, and Bobbin Depth. Use the data given below to determine if any of the factors have a statistically significant impact on average air flow.

Arm Length	Spring Load	Bobbin Depth	Air Flow
0.595	100	1.095	0.6
0.605	70	1.095	0.28
0.605	100	1.105	0.72
0.595	70	1.095	0.46
0.595	70	1.095	0.42
0.595	100	1.105	0.7
0.595	70	1.105	0.7
0.595	100	1.095	0.57
0.605	100	1.095	0.29
0.605	70	1.105	0.71
0.605	70	1.105	0.71
0.605	70	1.095	0.42
0.595	100	1.105	0.71
0.595	70	1.105	0.73
0.605	100	1.105	0.7
0.605	100	1.095	0.45

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Air Flow in Y input range and Arm Length, Spring Load and Bobbin Depth in X input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.916
R Square	0.839
Adjusted R Square	0.798
Standard Error	0.073
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	3	0.329	0.110	20.783	0.000
Residual	12	0.063	0.005
Total	15	0.392
	Coefficients	Standard Error	t Stat	P-value
Intercept	-25.074	4.552	-5.508	0.000
Arm Length	-7.625	3.632	-2.099	0.058
Spring Load	0.001	0.001	1.067	0.307
Bobbin Depth	27.375	3.632	7.537	0.000

For significance of each factor, conduct t-test:

1. Arm Length

H₀: β₁ = 0, Arm length does not have a statistically significant impact on average air flow

H₁: β₁ ≠ 0, Arm length has a statistically significant impact on average air flow

p-value = 0.058

Since p-value is more than 0.05, we do not reject the null hypothesis and conclude that β₁ = 0.

Arm length does not have a statistically significant impact on average air flow.

2. Spring Load

H₀: β₂ = 0, Spring load does not have a statistically significant impact on average air flow

H₁: β₂ ≠ 0, Spring load has a statistically significant impact on average air flow

p-value = 0.307

Since p-value is more than 0.05, we do not reject the null hypothesis and conclude that β₂ = 0.

Spring load does not have a statistically significant impact on average air flow.

3. Bobbin Depth

H₀: β₃ = 0, Bobbin depth does not have a statistically significant impact on average air flow

H₁: β₃ ≠ 0, Bobbin depth has a statistically significant impact on average air flow

p-value = 0.000

Since p-value is less than 0.05, we reject the null hypothesis and conclude that β₃ ≠ 0.

Bobbin depth has a statistically significant impact on average air flow.

Conclusion: Out of the 3 factors, only Bobbin Depth has a statistically significant impact on average air flow.