Reference no: EM133049254

Cost Analysis in the Technology Industry: A subsidiary of Elektra Electronics has developed new software that allows Windows-based personal computers to run all Apple (i.e., Mac, iPhone, iPad, etc.) and Android applications. Elektra has collected preliminary data on the weekly total cost of producing the new product at a number of different levels of production. Cost data are available in the worksheet entitled "Software Cost". 

a) Generate a scatterplot in order to understand the nature of the relationship between weekly quantity produced and weekly total cost. Use this information to complete the statements below.

According to the scatterplot, weekly total cost  --- decreases sharply remains the same increases sharply at first, then it  --- levels off decreases sharply increases sharply for a while, and then it begins to  --- decrease again increase again levels off , as the quantity produced increases. There appears to be bend(s) or curve(s) in the data which suggests that a  --- 2nd order polynomial reciprocal transformation 4th order polynomial logarithmic transformation 3rd order polynomial regression model is appropriate.

b) Use the data to fit three separate regression models. For the first model, fit the 2nd order polynomial regression model to predict weekly total cost. For the second model, fit the 3rd order polynomial regression model to predict weekly total cost. For the third model, fit the 4th order polynomial regression model to predict weekly total cost. 

Provide summary measures for each model separately in the table below. (Enter your R² values as percents to two decimal places and enter your standard errors to three decimal places.)

Model	R2	R2adj	se
Second-Order Model	%	%
Third-Order Model	%	%
Fourth-Order Model	%	%

According to your analysis so far, summarize your results.

According to R²_adj, the third-order model is clearly worse than either the second or fourth-order models, however, results are not so clear concerning whether the second or fourth-order model is best.According to R²_adj, the second-order model is clearly superior to either the third or fourth-order models.     According to R²_adj, the fourth-order model is clearly worse than either the second or third-order models, however, results are not so clear concerning whether the second or third-order model is best.According to R²_adj, the second-order model is clearly worse than either the third or fourth-order models, however, results are not so clear concerning whether the third or fourth-order model is best.According to R²_adj, the fourth-order model is clearly superior to either the second or third-order models.According to R²_adj, the third-order model is clearly superior to either the second or fourth-order models.

c) Perform the appropriate statistical test to test whether the fourth-order model explains a statistically significant amount of variation in total weekly cost above and beyond of that explained by the third-order model. Use a 5% significance level.

State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).

 ---Select--- G z t p F (  ) =  , p  ---Select--- > ≤ = ≥ < 

State your decision.

The fourth-order model explains a significant amount of variation in total weekly cost compared to the third-order model. Therefore, the fourth-order term in the model is not needed and a simpler model is preferred.The fourth-order model explains an insignificant amount of variation in total weekly cost compared to the third-order model. Therefore, the fourth-order term in the model is needed and the fourth-order model is best.     The fourth-order model explains a significant amount of variation in total weekly cost compared to the third-order model. Therefore, the fourth-order term in the model is needed and the fourth-order model is best.The fourth-order model explains an insignificant amount of variation in total weekly cost compared to the third-order model. Therefore, the fourth-order term in the model is not needed and a simpler model is preferred.

d) Regardless of your results above, assume that the third-order model is best. Based on this estimated total cost function, provide the estimated marginal total cost function (Enter all function coefficients to four decimal places).

C'(x) =

e) Compute the following quantities WITHOUT any intermediate rounding. In other words, do NOT use the rounded version of the function you reported above in part d. Instead, use the one stored in your EXCEL worksheet. Enter your answers to two decimal places.

How quickly is the weekly total cost increasing when the level of production is 100 units per week?

How quickly is the weekly total cost increasing when the level of production is 400 units per week?

How quickly is the weekly total cost increasing when the level of production is 725 units per week?

Quantity	Cost
110	15670.76
500	23405.66
120	18380.88
510	23145.39
340	23191.53
620	24464.14
350	22262.63
130	17012.08
510	23712.91
60	13728.09
80	14777.4
360	21645.45
110	15983.57
120	16254.58
230	20811.9
500	22145.26
650	25873.01
510	23094.15
90	14473.49
30	10810.92
250	20647.02
160	17342.48
710	27978.15
580	23724.68
560	23031.68
510	24193.06
340	22032.14
430	21703.87
660	25802.86
160	19589.52
360	23020.11
510	22350.73
520	22894.49
670	26330.24
510	23090.06
80	14072.29
740	30801.06
660	26305.13
250	20907.3
610	24660.3
380	21717.19
10	7132.79
760	30773.76
460	22831.66
380	22242.87
380	21411.74
250	18686.31
540	22751.03
430	21957.92
360	23092.64
550	23171.41
30	9890.3
300	20918.65
30	13103.14
120	17733.49
700	28261.58
690	27784.98
620	24911.21
800	36389.01
800	32989.9
360	21781.93
230	20480.66
520	21205.32
520	22512.59
510	24730.43
460	19778.44
370	22718.31
370	21864.31
390	22794.56
130	18682.11
80	14434.91
250	18966.93
130	17563.93
640	28181.57
400	22574.92
800	34484.12
430	22946.85
560	23943.21
620	24346.69
660	26324.26
30	10622.52
430	22247.62
550	23766.4
460	22794.75
30	11170.02
800	35079.01
110	15928.94
130	17397.95
300	23065.57
440	23248.85
400	21781.95
170	18099.79
120	16266.64
120	17441.66
540	22637.82
480	22443.35
160	17973.58
250	20820.46
510	22105.08
110	16005.45
520	22771.04
300	21372
380	21949.94
510	21284.16
620	23692.35
340	22329.97
550	23186.41
110	16214.73
380	21830.46
60	13411.67
360	21810.07
110	14902.48
430	22888.18
190	21034.96
430	22459.69
500	22541.96
620	24826.46
760	31807.33
250	21103.83
120	16178.64
370	22762.99
400	19607.21
70	12830.7
380	21656.21
510	22429.83
400	21939.05
20	9201.14
640	25381.11
740	29910.93
500	20920.47

Fuel Economy 2: Fuel economy data are available for all 50 states plus the District of Columbia. Build a regression model to forecast per capita fuel consumption in gallons (FUELCON) from the ratio of licensed drivers to private and commercial motor vehicles registered (DRIVERS), the number of miles of federally funded highways (HWYMILES), the tax per gallon of gasoline in cents (GASTAX), and the average household income in dollars (INCOME) and obtain the appropriate model diagnostic statistics: Use the Shapiro-Wilk test statistic to test the assumption of the normality of the model residuals. Use a 5% level of significance. The data can be found in the worksheet entitled "FUELCON4".

(a) State the model equation.

FUELCON = ??₁DRIVERS + ??₂HWYMILES + ??₃GASTAX + ??₄INCOMEDRIVERS = ??₀ + ??₁FUELCON + ??₂HWYMILES + ??₃GASTAX + ??₄INCOME     DRIVERS = ??₁FUELCON + ??₂HWYMILES + ??₃GASTAX + ??₄INCOMEFUELCON = ??₀ + ??₁DRIVERS + ??₂HWYMILES + ??₃GASTAX + ??₄INCOMEHWYMILES = ??₀ + ??₁FUELCON + ??₂FUELCON + ??₃GASTAX + ??₄DRIVERS
(b) What is being tested here? (Choose one) 

The assumption of constant variance.The assumption of independence.     Whether there is a linear relationship between x and y.Whether all of the x variables are important in predicting y.The assumption of normally-distributed disturbances.The assumption of linearity.
(c) Which hypotheses are being tested? (Choose one) 

H₀: The model variance is constant
H_a: The model variance is not constantH₀: All of the x variables in the model are not important
H_a: Atleast one of the x variables is important     H₀: ??₁ = 1.0
H_a: ??₁ ≠ 1.0H₀: Disturbances are normal
H_a: Disturbances are non-normalH₀: ??₁ = 0
H_a: ??₁ ≠ 0
(d) State the decision rule.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 > 0.10.
Do not reject H₀ if p ≤ 0.10.Reject H₀ if p > 0.05.
Do not reject H₀ if p ≤ 0.05.
(e) What is the name of the test statistic? (Choose one) 

Shapiro-Wilk's WTest of Constant Variance     Test of IndependenceThe Partial F TestKolmogorov-Smirnov's DAnderson-Darling's A²
(f) 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 W D A t F =  , p  ---Select--- < ≤ = ≥ > 
(g) What conclusion can be drawn from the test result?

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. There is a linear relationship between x and y.Do not reject H₀. The assumption of independence has been met.Do not reject H₀. The assumption of constant variance has been met.Reject H₀. The assumption of constant variance has not been met.Reject H₀. The assumption of normally-distributed disturbances has not been met.Do not reject H₀.The assumption of normally-distributed disturbances has been met.

OBSERVATION NUMBER	STATE	FUELCON	DRIVERS	HWYMILES	GASTAX	INCOME
1	Alabama	547.92	0.85	11,849	18	24426
2	Alaska	440.38	0.81	4,532	8	30997
3	Arizona	456.9	0.9	9,455	18	25479
4	Arkansas	530.08	1.07	7,949	21.7	22912
5	California	426.21	0.76	32,478	18	32678
6	Colorado	474.78	0.71	11,015	22	32957
7	Connecticut	432.44	0.92	3,820	25	41930
8	Delaware	492.97	0.88	1,260	23	32121
9	Florida	461.55	0.91	17,272	13.6	28493
10	Georgia	564.82	0.81	16,950	7.5	28438
11	Hawaii	336.97	0.92	1,089	16	28554
12	Idaho	484.83	0.69	6,466	25	24257
13	Illinois	406.99	0.8	19,700	19	32755
14	Indiana	524.01	0.74	10,261	15	27532
15	Iowa	532.39	0.61	10,037	20	27283
16	Kansas	483.31	0.81	10,494	21	28507
17	Kentucky	532.77	0.77	10,302	16.4	25057
18	Louisiana	513.8	0.77	8,954	20	24084
19	Maine	472.68	0.94	3,474	22	36385
20	Maryland	463.46	0.89	6,387	23.5	34950
21	Massachusetts	436.57	0.9	7,264	21	38845
22	Michigan	504.95	0.84	16,942	19	29538
23	Minnesota	532.52	0.66	12,509	20	32791
24	Mississippi	541.06	0.97	8,747	18.4	21643
25	Missouri	549.16	0.92	13,580	17	28029
26	Montana	549.35	0.68	10,456	27	23532
27	Nebraska	503.1	0.79	8,067	24.5	28564
28	Nevada	448.81	1.13	5,976	24.75	29860
29	New Hampshire	541.67	0.87	2,405	19.5	33928
30	New Jersey	465.52	0.89	9,150	10.5	38153
31	New Mexico	504.77	0.89	9,654	18.5	23162
32	New York	296.44	1.1	18,998	22	35884
33	North Carolina	510.05	0.97	13,632	24.1	27418
34	North Dakota	580.32	0.66	7,415	21	25538
35	Ohio	458.31	0.74	16,807	22	28619
36	Oklahoma	523.89	0.68	11,123	17	24787
37	Oregon	439.09	0.85	10,138	24	28000
38	Pennsylvania	417.36	0.87	18,448	26	30617
39	Rhode Island	382.82	0.88	1,037	29	29984
40	South Carolina	557.53	0.92	9,272	16	24594
41	South Dakota	577.84	0.7	7,753	22	26301
42	Tennessee	506.3	0.83	12,036	20	26758
43	Texas	502.17	0.93	49,678	20	28486
44	Utah	430.53	0.87	7,310	24.5	24202
45	Vermont	555.78	0.99	2,138	20	27992
46	Virginia	529.52	0.81	14,453	17.5	32295
47	Washington	446.63	0.83	10,802	23	31582
48	West Virginia	466.31	0.94	5,390	25.65	22725
49	Wisconsin	466.08	0.83	13,088	27.3	28911
50	Wyoming	715.55	0.67	7,841	14	28807
51	Washington D.C.	289.99	1.38	391	20	40498