Question

Question 2: A multiple linear regression analysis is performed and the following MINITAB output is observed: Regression Analysis: Fuel cell power versus H2 pressure and H2 flow The Regression Equation is Fuel cell power (W) = 2705.235 - 1.0745*H2 pressure (psi) + 3.7707*Hz flow (stoc) Term Coef SE Coef T-Value Constant 334.44 H2 pressure (psi) 9.09 Ha flow (stoc) 2.18 MS F-Value Analysis of Variance Source DF Regression Error Total 27 SS 3770.7 7751.78 Answer to the following questions based on the Minitab output. a) What is the multiple linear regression model? b) Write the fitted regression equation of this multiple linear regression. c) Fill the missing parts of the Minitab output. d) What conclusion can you draw about the regressor variable H2 flow (stoc) with a significance level of 0.05? Does it seem likely that this regressor contributes significantly to the model? e) Estimate the fuel cell power when H2 pressure and H2 flow readings are 2500 psi and 5, respectively. 1) Calculate coefficient of determination. Interpret it in the context of the problem.

Answer 1

a. Multiple linear regression model is the model that uses several explanatory variables specifically called as regressors to predict the value of response variable. Here the relation between regressors and response variable is almost linear.

b.

Here, Response variable: Fuel Cell Power

Regressor 1: H₂ pressure Regressor 2: H₂ flow

Fuel cell power = 2705.235 - 1.0745 * H₂ pressure + 3.7707 * H₂ flow

c.

To fill the missing part of Minitab output use following formulae,

$T.value=\frac{Coef}{SE.coef}$

$MSS=\frac{SS}{DF}$

Degrees of freedom for regression = number of regressors = 2

Error degrees of freedom = 27 - 2 = 25

Total SS = Regression SS + Error SS

Term	Coef	SE Coef	T-value
Constant	2705.235	334.44	8.088
H2 pressure	- 1.0745	9.09	-0.1182
H2 flow	3.7707	2.18	1.73

Analysis of Variance

Source	DF	SS	MSS	F
Regression	2	3770.7	1885.35	11.84
Error	25	3981.08	159.2432	-
Total	27	7751.78	-	-

d.

H₀: $\beta_i=0$ versus $\beta_i\neq 0$

To check the significance of variable H₂ flow we first calculate p-value

T-value for coefficient of H₂ flow = 1.73

Test statistic follows t distribution with n-p-1=25 degrees of freedom

P-value = P[ |t₂₅| > 1.73 ] = 0.09595 = 0.096

We reject H₀, at 0.05 level of significance if p-value < 0.05

Here, p-value > 0.05 hence, we do not reject H₀

We conclude that the regressor H₂ flow does not contribute significantly to the model.

e.

Givent that H₂ pressure = 2500 and H₂ flow = 5

Fuel cell power = 2705.235 - 1.0745 * H₂ pressure + 3.7707 * H₂ flow = 2705.235-1.0745*2500+3.7707*5

= 37.8385 w

Fuel cell power when Fuel cell power when H₂ pressure and H₂ flow readings are 2500 psi and 5 resp. is 37.8385 w.

f.

Coefficient of determination = $R^2=1-\frac{SSres}{SStotal}=1-\frac{3981.08}{7751.78}=0.48643$

48.643% percentage of variation in fuel cell power is explained by the regression model.

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