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
H_a: β₁ ≠ 1.0H₀: All of the x variables in the model are not important
H_a: Atleast one of the x variables is important    H₀: The model variance is constant
H_a: The model variance is not constantH₀: Disturbances are normal
H_a: Disturbances are non-normalH₀: β₁ = 0
H_a: 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

Answer 1