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Q1. 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.
Q2. 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 |
- Set up the opportunity loss table based on the provided payoff figures.
- 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.
Q3. Using the following data and analyze in EXCEL.
Table
a. Which pattern is visible in all the crops across these many years? Suggest appropriate chart for this pattern detection task.
b. Identify two pairs of combination of the crops having negative correlations? Which graph will help you to detect that? provide that graph also.