The brake horsepower developed by an automobile engine on a dynamometer is thoug

Question

The brake horsepower developed by an automobile engine on a dynamometer is thought to be a function of the engine speed in revolutions per minute (rpm), the road octane number of the fuel, and the engine compression. An experiment is run in the laboratory and the data are drawn in Table 4:
(a) Fit a multiple regression model to these data.
(b) Test for significance of regression. What conclusions can you draw?
(c) Based on t-tests, do you need all three regressor variables in the model? aste Clipboard Font Alignment E24 1 Brake Horse Power RPM Road Octane Number Compression 225 2000 212 1800 229 2400 222 1900 219 1600 278 2500 246 3000 237 3200 233 2800 224 3400 223 1800 230 2500 90 100 94 110 91 86 96 100 110 98 100 105 97 100 104 90 86 90 89 16 17 ent 29298673430 2 2 2 2 2 2 2 2 2 2 2 pmd Co Fo 1234567890 11 12 13 14 15

Explanation / Answer

a) Multiple regression model:

Break Horse Power = -266.03121 + 0.01071 RPM + 3.13481 Road Octane Number

+ 1.86741 Compression

b) Significance of regression:

Hypothesis:

H0: all regression coefficients equals to zero

H1: at least one coefficient is not equal to zero

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -2.660e+02 9.267e+01 -2.871 0.02081 *

rpm 1.071e-02 4.483e-03 2.390 0.04388 *

ro 3.135e+00 8.444e-01 3.712 0.00594 **

com 1.867e+00 5.345e-01 3.494 0.00816 **

Residual standard error: 8.812 on 8 degrees of freedom

Multiple R-squared: 0.8065, Adjusted R-squared: 0.734

F-statistic: 11.12 on 3 and 8 DF, p-value: 0.00317

Here we see that p value for model is 0.00317 which is less than 0.05. So at 5% l.o.s. we reject H0 and conclude that at least one regression coefficient is not equal to zero.

c) Conclusions based on t test:

Hypothesis:

H0: i = 0

H1: i 0 i= 1,2,3

Table value of t with 8 degrees of freedom at 5% l.o.s. is 2.306. We compare t value of all 3 variable to 2.306. We observe that all t value are greater than 2.306. So in each case we accept alternative hypothesis that all ’s are significantly different from zero.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.