Business Statistics - NMIMS

 

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NMIMS Global Access

School for Continuing Education (NGA-SCE)

Course:  Business Statistics

Internal Assignment Applicable for September 2020 Examination

Assignment Marks: 30

Instructions:

·       All Questions carry equal marks.

·       All Questions are compulsory

·       All answers to be explained in not more than 1000 words for question 1 and 2 and for question 3 in not more than 500 words for each subsection. Use relevant examples, illustrations as far aspossible.

·       All answers to be written individually. Discussion and group work is not advisable.

·       Students are free to refer to any books/reference material/website/internet for attempting theirassignments, but are not allowed to copy the matter as it is from the source of reference.

·       Students should write the assignment in their own words. Copying of assignments from otherstudents is not allowed.

·       Students should follow the following parameter for answering the assignment questions.

 

For Theoretical Answer			For Numerical Answer
Assessment Parameter	Weightage		Assessment Parameter	Weightage
Introduction	20%		Understanding and usage of the formula	20%
Concepts and Application related to the question	60%		Procedure / Steps	50%
Conclusion	20%		Correct Answer & Interpretation	30%

 

 

Question 1: Data Set:

Sample of 7 different species of fish has been taken and their weight in grams, lengths (vertical, diagonal, cross given as length 1, length 2 and length 3 respectively), height and width in cm is given below:

 

Species	Weight	Length1	Length2	Length3	Height	Width
Bream	725	31.8	35	40.9	16.36	6.0532
Bream	720	32	35	40.6	16.3618	6.09
Bream	714	32.7	36	41.5	16.517	5.8515
Bream	850	32.8	36	41.6	16.8896	6.1984
Bream	1000	33.5	37	42.6	18.957	6.603
Bream	920	35	38.5	44.1	18.0369	6.3063
Bream	955	35	38.5	44	18.084	6.292
Bream	925	36.2	39.5	45.3	18.7542	6.7497
Bream	975	37.4	41	45.9	18.6354	6.7473
Bream	950	38	41	46.5	17.6235	6.3705
Roach	0	19	20.5	22.8	6.4752	3.3516
Roach	110	19.1	20.8	23.1	6.1677	3.3957
Roach	120	19.4	21	23.7	6.1146	3.2943
Roach	150	20.4	22	24.7	5.8045	3.7544
Roach	145	20.5	22	24.3	6.6339	3.5478
Roach	160	20.5	22.5	25.3	7.0334	3.8203
Roach	140	21	22.5	25	6.55	3.325
Roach	160	21.1	22.5	25	6.4	3.8
Roach	169	22	24	27.2	7.5344	3.8352
Roach	161	22	23.4	26.7	6.9153	3.6312
Roach	200	22.1	23.5	26.8	7.3968	4.1272
Roach	180	23.6	25.2	27.9	7.0866	3.906
Roach	290	24	26	29.2	8.8768	4.4968
Roach	272	25	27	30.6	8.568	4.7736
Roach	390	29.5	31.7	35	9.485	5.355
Whitefish	270	23.6	26	28.7	8.3804	4.2476
Whitefish	270	24.1	26.5	29.3	8.1454	4.2485
Whitefish	306	25.6	28	30.8	8.778	4.6816
Whitefish	540	28.5	31	34	10.744	6.562
Whitefish	800	33.7	36.4	39.6	11.7612	6.5736
Whitefish	1000	37.3	40	43.5	12.354	6.525
Parkki	55	13.5	14.7	16.5	6.8475	2.3265
Parkki	60	14.3	15.5	17.4	6.5772	2.3142
Parkki	90	16.3	17.7	19.8	7.4052	2.673
Parkki	120	17.5	19	21.3	8.3922	2.9181
Parkki	150	18.4	20	22.4	8.8928	3.2928
Parkki	140	19	20.7	23.2	8.5376	3.2944
Parkki	170	19	20.7	23.2	9.396	3.4104
Parkki	145	19.8	21.5	24.1	9.7364	3.1571
Parkki	200	21.2	23	25.8	10.3458	3.6636
Parkki	273	23	25	28	11.088	4.144
Parkki	300	24	26	29	11.368	4.234
Perch	5.9	7.5	8.4	8.8	2.112	1.408
Perch	32	12.5	13.7	14.7	3.528	1.9992
Perch	40	13.8	15	16	3.824	2.432
Perch	51.5	15	16.2	17.2	4.5924	2.6316
Perch	70	15.7	17.4	18.5	4.588	2.9415
Perch	100	16.2	18	19.2	5.2224	3.3216
Perch	78	16.8	18.7	19.4	5.1992	3.1234
Perch	80	17.2	19	20.2	5.6358	3.0502
Perch	85	17.8	19.6	20.8	5.1376	3.0368
Perch	85	18.2	20	21	5.082	2.772
Perch	110	19	21	22.5	5.6925	3.555
Pike	430	35.5	38	40.5	7.29	4.5765
Pike	345	36	38.5	41	6.396	3.977
Pike	456	40	42.5	45.5	7.28	4.3225
Pike	510	40	42.5	45.5	6.825	4.459
Pike	540	40.1	43	45.8	7.786	5.1296
Pike	500	42	45	48	6.96	4.896
Pike	567	43.2	46	48.7	7.792	4.87
Pike	770	44.8	48	51.2	7.68	5.376
Pike	950	48.3	51.7	55.1	8.9262	6.1712
Pike	1250	52	56	59.7	10.6863	6.9849
Smelt	6.7	9.3	9.8	10.8	1.7388	1.0476
Smelt	7.5	10	10.5	11.6	1.972	1.16
Smelt	7	10.1	10.6	11.6	1.7284	1.1484
Smelt	9.7	10.4	11	12	2.196	1.38
Smelt	9.8	10.7	11.2	12.4	2.0832	1.2772
Smelt	8.7	10.8	11.3	12.6	1.9782	1.2852
Smelt	10	11.3	11.8	13.1	2.2139	1.2838
Smelt	9.9	11.3	11.8	13.1	2.2139	1.1659
Smelt	9.8	11.4	12	13.2	2.2044	1.1484
Smelt	12.2	11.5	12.2	13.4	2.0904	1.3936

 

Q1: Find the mean and standard deviation for each type of fish for every variable.

Answer: 1. To compute the mean and standard deviation we will use the below formulas.

The mean   is computed as follows,

Also, the sample variance is,

 

 

Question 2. If you need to choose a fish on the basis of weight, which fish you choose?

Answer   : The mean and standard deviation for Weight variable for all species is below:

 

Species	Mean	Standard Deviation
Bream	873.4	113.1471019
Roach	176.4666667	88.95574073
Whitefish	531	309.6029716
Parkki	154.8181818	78.75508642

 

 

 

Question.3. Find mean, median, quartiles for the entire data set for each variable. (10 marks)

Answer :  Mean:

 

 By using the same formula as in part (a), the mean are,

 

The sample size is n = 73. The provided sample data along with the data required to compute the sample mean  for each variable of all species is shown in the table below:

Mean

 

 

Question 2 : Regress the following: (10 Marks)

1. Taking weight as dependent variable and height as independent variable. Is variable is found to be significant?

Answer :  Below is the output:

Regression Statistics
Multiple R	0.094799718

2. Taking weight as dependent variable and width as independent variable. Is variable is found to be significant?

Answer : 

Regression Statistics
Multiple R	0.913804714
R Square	0.835039055

 

3. Taking weight as dependent variable and length1, length 2 and length 3 as independent variable. Are variables is found to be significant? Which variable is not significant?

Answer : 

Regression Statistics
Multiple R	0.938718572
R Square	0.881192557
Adjusted R Square	0.876027017

 

4. Taking weight as dependent variable and height, width, length 1, length 2 and length 3 as independent variable.

Answer : 

Regression Statistics
Multiple R	0.940567787
R Square	0.884667763
Adjusted R Square	0.876060879
Standard Error	117.7864532
Observations	73
ANOVA
	df	SS	MS	F	Significance F
Regression	5	7130089.418	1426017.884	102.7860752	4.85005E-30

5. On basis of adjusted R square compare the model of part a, b, c and d. which model is best to predict weight?

Models	Adjusted R Square
a)       Weight vs Height	-0.004970943
b)       Weight vs Width	0.832715661

 

 

 

 

Question 3.  The daily COVID 19 cases (in hundred) for Delhi for past 2 week is summarize in the following table:

Day	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Cases	28	29	33	31	37	34	36	43	41	32	34	37	39	32

 

 

1. Using exponential smoothing method forecast the cases for 15 days, taking alpha as 0.3 and Initial forecast is the average of all data. (5 Marks)

Answer : First we need to compute mean of the data.

The mean   is computed as follows,

   Mean = (1/14)* 486 = 34.7142857.

2. Using linear trend analysis, find the trend line for number of COVID 19 cases in Delhi and forecast for next 3 days. Also compute the Mean Square Error. (5 Marks)

Answer : The independent variable is Time, and the dependent variable is Cases. In order to compute the regression coefficients, the following table needs to be used:

 

	Days (X)	Cases (Y)	Days*Cases (XY)	Days^2 (X^2)	Cases^2 (Y^2)
	1	28	28	1	784
	2	29	58	4	841
	3	33	99	9	1089
	4	31	124	16	961
	5	37	185	25	1369
	6	34	204	36	1156
	7	36	252	49	1296
	8	43	344	64	1849
	9	41	369	81	1681
	10	32	320	100	1024
	11	34	374	121	1156
	12	37	444	144	1369
	13	39	507	169	1521
	14	32	448	196	1024
Sum =	105	486	3756	1015	17120

 

 

Hello MBA aspirants,

Get MBA assignments of NMIMS University solved by educational professionals at a nominal charge.

Mail us at: help.mbaassignments@gmail.com

Call us at: 08263069601