The data shown in the following table represent the trust of a jet-turbine engin

Question

The data shown in the following table represent the trust of a jet-turbine engine (y) and six candidate regressors: x1 = primary speed of rotation, x2 = secondary speed of rotation, x3 = fuel flow rate, x4 = pressure, x5 = exhaust temperature, and x6 = ambient temperature at the time of the test.

Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to two decimal places (e.g. 98.76).

(a) Fit the model using y* = ln y as the response and x*3 = ln x3, x4, and x5 as the regressors.

Obs. No. y x1 x2 x3 x4 x5 x6 1 4540 2140 20640 30250 205 1732 99 2 4315 2016 20280 30010 195 1697 100 3 4095 1905 19860 29780 184 1662 97 4 3650 1675 18980 29330 164 1598 97 5 3200 1474 18100 28960 144 1541 97 6 4833 2239 20740 30083 215 1709 87 7 4617 2120 20305 29831 206 1669 87 8 4340 1990 19961 29604 195 1640 87 9 3820 1702 18916 29088 171 1572 85 10 3368 1487 18012 28675 149 1522 85 11 4445 2107 20520 30120 195 1740 101 12 4188 1973 20130 29920 190 1711 100 13 3981 1864 19780 29720 180 1682 100 14 3622 1674 19020 29370 161 1630 100 15 3125 1440 18030 28940 139 1572 101 16 4560 2165 20680 30160 208 1704 98 17 4340 2048 20340 29960 199 1679 96 18 4115 1916 19860 29710 187 1642 94 19 3630 1658 18950 29250 164 1576 94 20 3210 1489 18700 28890 145 1528 94 21 4330 2062 20500 30190 193 1748 101 22 4119 1929 20050 29960 183 1713 100 23 3891 1815 19680 29770 173 1684 100 24 3467 1595 18890 29360 153 1624 99 25 3045 1400 17870 28960 134 1569 100 26 4411 2047 20540 30160 193 1746 99 27 4203 1935 20160 29940 184 1714 99 28 3968 1807 19750 29760 173 1679 99 29 3531 1591 18890 29350 153 1621 99 30 3074 1388 17870 28910 133 1561 99 31 4350 2071 20460 30180 198 1729 102 32 4128 1944 20010 29940 186 1692 101 33 3940 1830 19640 29750 178 1667 101 34 3480 1612 18710 29360 156 1609 101 35 3064 1410 17780 28900 136 1552 101 36 4402 2066 20520 30170 197 1758 100 37 4180 1954 20150 29950 188 1729 99 38 3973 1835 19750 29740 178 1690 99 39 3530 1616 18850 29320 156 1616 99 40 3080 1407 17910 28910 137 1569 100

Explanation / Answer

The data shown in the following table represent the trust of a jet-turbine engine (y) and six candidate regressors: x1 = primary speed of rotation, x2 = secondary speed of rotation, x3 = fuel flow rate, x4 = pressure, x5 = exhaust temperature, and x6 = ambient temperature at the time of the test.

Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to two decimal places (e.g. 98.76).

Regression Analysis

R²

0.991

Adjusted R²

0.990

n

40

R

0.995

k

3

Std. Error

0.013

Dep. Var.

lny

ANOVA table

Source

SS

df

MS

F

p-value

Regression

0.6861

3  

0.2287

1321.39

7.30E-37

Residual

0.0062

36  

0.0002

Total

0.6923

39  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=36)

p-value

99% lower

99% upper

Intercept

21.0682

9.6494

2.183

.0356

-5.1731

47.3095

lnx3

-1.4040

0.9656

-1.454

.1546

-4.0298

1.2218

x4

0.0055

0.00027515

19.951

4.74E-21

0.0047

0.0062

x5

0.00041786

0.00016489

2.534

.0158

-0.00003056

0.00086628

(a) Fit the model using y* = ln y as the response and x*3 = ln x3, x4, and x5 as the regressors.

lny = 21.0682-1.4040*lnx3+0.0055x4+0.00041786*x5

(b) Test for significance of regression using = 0.01.

Calculated F=1321.39, P=0.0000 which is < 0.01 level of significance.

The model is significant.

Calculate f0

© Use the t-statistic to test H0: j = 0 versus H0: bj 0. Use a = 0.01.

b*3 :

Calculate t0.

-1.45

Do not reject H0

b4 :

Calculate t0.

19.95

Reject H0

b5 :

Calculate t0.

2.53

Do not reject H0

Regression Analysis

R²

0.991

Adjusted R²

0.990

n

40

R

0.995

k

3

Std. Error

0.013

Dep. Var.

lny

ANOVA table

Source

SS

df

MS

F

p-value

Regression

0.6861

3  

0.2287

1321.39

7.30E-37

Residual

0.0062

36  

0.0002

Total

0.6923

39  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=36)

p-value

99% lower

99% upper

Intercept

21.0682

9.6494

2.183

.0356

-5.1731

47.3095

lnx3

-1.4040

0.9656

-1.454

.1546

-4.0298

1.2218

x4

0.0055

0.00027515

19.951

4.74E-21

0.0047

0.0062

x5

0.00041786

0.00016489

2.534

.0158

-0.00003056

0.00086628

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