2 Problem 107 in course text For this problem Brake Horsepow

2. Problem 10.7 in course text. For this problem, Brake Horsepower is the response. The linear model to fit is Brake Horsepower = f(rpm, Road Octane Number, Compression).

Solution

Let response variable y = Brake Horsepower

x1 = revolutions per minute (rpm)

x2 = Road octane number.

x3 = Compression

We answer all the questions by using MINITAB.

Enter all the data in MINITAB.

STAT --> Regression --> Regression --> Response : y --> Predictors : x1,x2,x3 --> Results : select second option --> ok --> ok

This will gives us the following output as,

Welcome to Minitab, press F1 for help.

Regression Analysis: y versus x1, x2, x3

The regression equation is
y = - 266 + 0.0107 x1 + 3.13 x2 + 1.87 x3

Predictor Coef SE Coef T P
Constant -266.03 92.67 -2.87 0.021
x1 0.010713 0.004483 2.39 0.044
x2 3.1348 0.8444 3.71 0.006
x3 1.8674 0.5345 3.49 0.008

S = 8.81239 R-Sq = 80.7% R-Sq(adj) = 73.4%

Analysis of Variance

Source DF SS MS F P
Regression 3 2589.73 863.24 11.12 0.003
Residual Error 8 621.27 77.66
Total 11 3211.00

Test for significance of regression :

Assume alpha = level of significance = 5% = 0.05

We see that P-value for x1, x2 and x3 is 0.044, 0.006 anf 0.008 respectively.

All the P-values are less than alpha (0.05).

Reject H0 at 5% level of significance.

Conclusion : Population regression coefficient for x1, x2 and x3 are differ than 0.

Thus we include all the three regressors in the model.