Decision Science June 2024

Description

Decision Science

June 2024 Examination

 

 

1. In the world of social media, understanding the factors that contribute to the number of likes on a post is crucial for content creators. Let’s consider a scenario where you want to predict the number of likes on Instagram posts based on two variables: the number of followers and the length of the caption.

Post	Likes	Followers	Caption   Length
1	120	5000	150
2	85	5500	180
3	100	6000	200
4	110	4500	160
5	95	7000	140
6	130	5200	170
7	75	5800	190
8	115	6300	150
9	80	4800	180
10	150	7500	160
11	105	5100	130
12	90	6700	170
13	125	5900	200
14	70	6800	150
15	140	5400	180
16	95	7200	160
17	120	4600	140
18	110	7100	170
19	100	5600	180
20	145	8000	120

 

Note:

Well, you must do these calculations using EXCEL and write the interpretation of the following.

• Hypothesized regression model
• R-square adjusted
• Multiple R
• ANOVA Table
• Significance of Regression coefficients. (10 Marks)

Ans 1.

Introduction

In the digital age, social media platforms like Instagram have become critical venues for content dissemination, enabling users to engage with a global audience. For content creators, understanding what drives engagement on their posts is essential. Engagement, typically measured by the number of likes, can be influenced by various factors such as the content’s reach and its appeal. In this study, we focus on predicting the number of likes an Instagram post might receive based on two specific variables: the number of followers the poster has and the length of the post’s caption

 

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2.Samantha  Patel,  employed  as  an   analyst  in  a  renowned  technology  firm,  is contemplating investing her savings in the stock market. Recommendations from her friends, who possess expertise in stock market investments, led her to consider investing in

‘TechGen’ and ‘InnovateCorp’ shares. An economist friend, Rahul Kapoor, has outlined four different scenarios regarding potential returns on Samantha’s investments. The payoff figures for one unit of share in INR for each scenario are as follows:

Payoff (Profit within one month   on one unit of share in INR)	Scenario 1   (s1)	Scenario 2   (s2)	Scenario 3   (s3)	Scenario 4   (s4)
TechGen	48	35	22	15
InnovateCorp	32	40	45	53

 

1. Set up the opportunity loss table based on the provided payoff figures.
2. Create a decision  tree  illustrating  the  decision-making  process  for  Samantha’s investment. You may use any software for making the tree diagram, but a handwritten snapshot will be unacceptable.

In making of this tree show the payoff values given above only.

iii.  According  to  Rahul  Kapoor’s  latest  research,  he  has  assigned  the  following probabilities to the four scenarios (states of nature):

• P(S1) = 0.3
• P(S2) = 0.4
• P(S3) = 0.2
• P(S4) = 0.1

Determine   the   Expected   Monetary   Value   (EMV)   decision   based   on   the probabilities assigned by Rahul. (10 Marks)

Ans 2.

Introduction

Making informed decisions in stock investments requires careful consideration of various scenarios and their associated potential payoffs. Samantha Patel, an analyst at a prominent technology firm, is considering investing in shares from two companies, TechGen and InnovateCorp. Given the volatile nature of the stock market, understanding the expected outcomes based on different economic conditions can significantly aid in decision-making. To assist Samantha, an opportunity loss table, a decision tree, and the calculation of the Expected Monetary Value (EMV) will be developed. These tools will not only visualize possible outcomes and their likelihoods but also quantify the expected returns, helping Samantha make a more data

 

 

3. Using the following data and analyze in EXCEL.

Year	Rice (Lakh   hectares)	Wheat   (Lakh hectares)	Coarse   Cereals (Lakh hectares)	Pulses   (Lakh hectares)
1966-67	353	128	451	221
1967-68	364	150	473	227
1968-69	370	160	462	213
1969-70	377	166	472	220

 

Year	Rice (Lakh   hectares)	Wheat   (Lakh hectares)	Coarse   Cereals (Lakh hectares)	Pulses   (Lakh hectares)
1970-71	376	182	460	225
1971-72	378	191	436	222
1972-73	367	195	422	209
1973-74	383	186	462	234
1974-75	379	180	432	220
1975-76	395	205	438	245
1976-77	385	209	419	230
1977-78	403	215	423	235
1978-79	405	226	422	237
1979-80	394	222	414	223
1980-81	402	223	418	225
1981-82	407	221	425	238
1982-83	383	236	404	228
1983-84	412	247	417	235
1984-85	412	236	392	227

 

Year	Rice (Lakh   hectares)	Wheat   (Lakh hectares)	Coarse   Cereals (Lakh hectares)	Pulses   (Lakh hectares)
1985-86	411	230	395	244
1986-87	412	231	397	232
1987-88	388	231	366	213
1988-89	417	241	387	232
1989-90	422	235	377	234
1990-91	427	242	363	247
1991-92	427	233	334	225
1992-93	418	246	344	224
1993-94	425	252	328	223
1994-95	428	257	322	230
1995-96	428	250	309	223
1996-97	434	259	318	225
1997-98	435	267	308	229
1998-99	448	275	293	235
1999-00	452	275	293	211

 

 

Year	Rice (Lakh   hectares)	Wheat   (Lakh hectares)	Coarse   Cereals (Lakh hectares)	Pulses   (Lakh hectares)
2000-01	447	257	303	204
2001-02	449	263	295	220
2002-03	412	252	270	205
2003-04	426	266	308	235
2004-05	419	264	290	228
2005-06	437	265	291	224
2006-07	438	280	287	232
2007-08	439	280	285	236
2008-09	455	278	275	221
2009-10	419	285	277	233
2010-11	429	291	283	264
2011-12	440	299	264	245
2012-13	428	300	248	233
2013-14	440	312	257	252
2014-15	439	310	242	231

 

 

Year	Rice (Lakh   hectares)	Wheat   (Lakh hectares)	Coarse   Cereals (Lakh hectares)	Pulses   (Lakh hectares)
2015-16	435	304	244	249
2016-17	440	308	250	294
2017-18	438	297	243	298
2018-19	442	293	221	292
2019-20	437	314	240	280
2020-21	458	311	241	288
2021-22	463	305	227	307
2022-23	477	318	236	291

 

Data source: RBI

1. Which pattern is visible in all the crops across these many years? Suggest appropriate chart for this pattern detection task. (5 Marks)

Ans 3a.

Introduction

Analyzing agricultural data across several decades provides insights into the cropping patterns and trends which are crucial for policy making and strategic agricultural planning. The data from RBI on crop cultivation area across different years for rice, wheat, coarse cereals, and pulses allows

 

1. Identify two pairs of combination of the crops having negative correlations? Which graph will help you to detect that? provide that graph also. (5 Marks)

Ans 3b.

Introduction

Exploring correlations between different crops’ cultivation areas can uncover relationships that might indicate competitive or complementary planting strategies among farmers. Identifying pairs of crops with negative correlations helps in understanding how the increase in the area of one crop might coincide with the decrease in another, possibly reflecting shifts in farmer preferences or market demands over ti