The data worksheet entitled FUELCON4 contains the following variables for all 50 states plus the District of
Question:
The data worksheet entitled "FUELCON4" contains the following variables for all 50 states plus the District of Columbia.
| FUELCON (y): | Per capita fuel consumption in gallons |
| DRIVERS (x1): | The ratio of licensed drivers to private and commercial motor vehicles registered |
| HWYMILES (x2): | The number of miles of federally funded highways |
| GASTAX (x3) : | The tax per gallon of gasoline in cents |
| INCOME (x4): | The average household income in dollars |
Run the regression analysis with FUELCON as the dependent variable and the other four variables as independent variables and obtain the appropriate model diagnostic statistics: Use the Shapiro-Wilk teststatistic to test the assumption of the normality of the model residuals.
(a) What is being tested here? (Choose one)
The assumption of linearity.The assumption of normally-distributed disturbances. Whether there is a linear relationship between x and y.The assumption of constant variance.The assumption of independence. Whether all of the x variables are important in predicting y.
(b) Which hypotheses are being tested? (Choose one)
H0: β1 = 1.0
Ha: β1 ≠ 1.0H0: All of the x variables in the model are not important
Ha: Atleast one of the x variables is important H0: The model variance is constant
Ha: The model variance is not constantH0: Disturbances are normal
Ha: Disturbances are non-normalH0: β1 = 0
Ha: β1 ≠ 0
(c) State the decision rule.
Reject H0 if p < 0.10.
Do not reject H0 if p ≥ 0.10.Reject H0 if p > 0.10.
Do not reject H0 if p ≤ 0.10. Reject H0 if p < 0.05.
Do not reject H0 if p ≥ 0.05.Reject H0 if p > 0.05.
Do not reject H0 if p ≤ 0.05.
(d) What is the name of the test statistic? (Choose one)
Anderson-Darling's A2Shapiro-Wilk's W Test of Constant VarianceKolmogorov-Smirnov's DThe Partial F TestTest of Independence
(e) State the appropriate test statistic name, test statistic value, and the associated p-value (Enter the test statistic value to three decimal places, and the p-value to four decimal places).
---Select--- z A D F t W = , p ---Select--- < ≥ ≤ > =
(f) What conclusion can be drawn from the test result?
Do not reject H0.The assumption of normally-distributed disturbances has been met.Do not reject H0. The assumption of independence has been met. Reject H0. There is a linear relationship between x and y.Reject H0. The assumption of independence has not been met.Do not reject H0. There is not a linear relationship between x and y.Reject H0. The assumption of constant variance has not been met.Do not reject H0. The assumption of constant variance has been met.Reject H0. The assumption of normally-distributed disturbances has not been met.
| FUELCON | DRIVERS | HWYMILES | GASTAX | INCOME |
| 547.92 | 0.85 | 11,849 | 18 | 24426 |
| 440.38 | 0.81 | 4,532 | 8 | 30997 |
| 456.9 | 0.9 | 9,455 | 18 | 25479 |
| 530.08 | 1.07 | 7,949 | 21.7 | 22912 |
| 426.21 | 0.76 | 32,478 | 18 | 32678 |
| 474.78 | 0.71 | 11,015 | 22 | 32957 |
| 432.44 | 0.92 | 3,820 | 25 | 41930 |
| 492.97 | 0.88 | 1,260 | 23 | 32121 |
| 461.55 | 0.91 | 17,272 | 13.6 | 28493 |
| 564.82 | 0.81 | 16,950 | 7.5 | 28438 |
| 336.97 | 0.92 | 1,089 | 16 | 28554 |
| 484.83 | 0.69 | 6,466 | 25 | 24257 |
| 406.99 | 0.8 | 19,700 | 19 | 32755 |
| 524.01 | 0.74 | 10,261 | 15 | 27532 |
| 532.39 | 0.61 | 10,037 | 20 | 27283 |
| 483.31 | 0.81 | 10,494 | 21 | 28507 |
| 532.77 | 0.77 | 10,302 | 16.4 | 25057 |
| 513.8 | 0.77 | 8,954 | 20 | 24084 |
| 472.68 | 0.94 | 3,474 | 22 | 36385 |
| 463.46 | 0.89 | 6,387 | 23.5 | 34950 |
| 436.57 | 0.9 | 7,264 | 21 | 38845 |
| 504.95 | 0.84 | 16,942 | 19 | 29538 |
| 532.52 | 0.66 | 12,509 | 20 | 32791 |
| 541.06 | 0.97 | 8,747 | 18.4 | 21643 |
| 549.16 | 0.92 | 13,580 | 17 | 28029 |
| 549.35 | 0.68 | 10,456 | 27 | 23532 |
| 503.1 | 0.79 | 8,067 | 24.5 | 28564 |
| 448.81 | 1.13 | 5,976 | 24.75 | 29860 |
| 541.67 | 0.87 | 2,405 | 19.5 | 33928 |
| 465.52 | 0.89 | 9,150 | 10.5 | 38153 |
| 504.77 | 0.89 | 9,654 | 18.5 | 23162 |
| 296.44 | 1.1 | 18,998 | 22 | 35884 |
| 510.05 | 0.97 | 13,632 | 24.1 | 27418 |
| 580.32 | 0.66 | 7,415 | 21 | 25538 |
| 458.31 | 0.74 | 16,807 | 22 | 28619 |
| 523.89 | 0.68 | 11,123 | 17 | 24787 |
| 439.09 | 0.85 | 10,138 | 24 | 28000 |
| 417.36 | 0.87 | 18,448 | 26 | 30617 |
| 382.82 | 0.88 | 1,037 | 29 | 29984 |
| 557.53 | 0.92 | 9,272 | 16 | 24594 |
| 577.84 | 0.7 | 7,753 | 22 | 26301 |
| 506.3 | 0.83 | 12,036 | 20 | 26758 |
| 502.17 | 0.93 | 49,678 | 20 | 28486 |
| 430.53 | 0.87 | 7,310 | 24.5 | 24202 |
| 555.78 | 0.99 | 2,138 | 20 | 27992 |
| 529.52 | 0.81 | 14,453 | 17.5 | 32295 |
| 446.63 | 0.83 | 10,802 | 23 | 31582 |
| 466.31 | 0.94 | 5,390 | 25.65 | 22725 |
| 466.08 | 0.83 | 13,088 | 27.3 | 28911 |
| 715.55 | 0.67 | 7,841 | 14 | 28807 |
| 289.99 | 1.38 | 391 | 20 | 40498 |
Expert Answer:
a The test being tested here is Answer The assumption of normally distributed disturbances ... View the full answer
