7318AFE: Business Data Analytics Report - Life Insurance and Longevity - Business Assignment Help

Assignment Task:

QUESTION A1 (10 marks)

In the last part of the 20th century, scientists developed the theory that the planet was warming and that the primary cause was the increasing amounts of atmospheric carbon dioxide (CO2), which are the product of burning oil, natural gas, and coal (fossil fuels). Although many climatologists believe in the so-called greenhouse effect, many others do not subscribe to this theory. There are three critical questions that need to be answered in order to resolve the issue.

• Is Earth actually warming? 

• If Earth is warming, is CO2 the cause? There are greenhouse gases in the atmosphere, without which Earth would be considerably colder. These gases include methane, water vapour, and carbon dioxide. All occur naturally in nature. Carbon dioxide is vital to our life on Earth because it is necessary for growing plants. The amount of CO2 produced by fossil fuels is a relatively small proportion of all the CO2 in the atmosphere. 

The generally accepted procedure is to record monthly temperature anomalies. To do so, we calculate the average for each month over many years. We then calculate any deviations between the latest month’s temperature reading and its average. A positive anomaly would represent a month’s temperature that is above the average. A negative anomaly indicates a month where the temperature is less than the average. GLOBAL.xlsx stores the monthly data for temperature anomalies (0C) and the CO2 levels (ppm) in the atmosphere from Mar 1958 to November 2009. There are two issues in this discussion. First, is there global warming; second, if so, is carbon dioxide the cause?

• Is Earth actually warming?                                                                                                                                                                                           

1. Considering the temperature anomalies data over the data period 1958-2009, use a graphical technique to show whether there is global warming.                                     

2. Considering the average of the temperature anomalies, test to show that, on average, at the 5 percent level of significance, there is global warming. That is the mean temperature anomalies is positive (μ > 0)?                                                                                       

• If Earth is warming, is CO2 the cause?

3. Use a graphical technique to determine whether there is a relationship between temperature anomalies and CO2 levels. Interpret the results.                               

4. Find the correlation between temperature anomalies and CO2 levels. Interpret the results. 

5. Calculate the least squares line between temperature anomalies and CO2 levels. Interpret the findings.                                                                         

QUESTION A2: Are e-grocer sales profitable? [4 marks]

Companies that sell groceries over the internet are called e-grocers. Customers enter their orders, pay by credit card, and receive delivery by truck. A potential e-grocer analysed the market and determined that to be profitable the average order would have to exceed $85. To determine whether an e-grocery would be profitable in one large city, the service was offered to a random sample of customers and the size of the orders recorded in file ORDERS.xlsx. Can we infer from these data that an e-grocery will be profitable in this city?

QUESTION A3: Do higher interest rates reduce the availability of new housing? [4 marks]

A homebuilders’ association lobbying for various home subsidy programs argued that, during periods of high interest rates, the number of building permits issued decreased drastically, which in turn reduced the availability of new housing. The raw data are recorded in file HOUSE.xlsx were presented as part of their argument. Analyse the data.

QUESTION A4:  Life Insurance and Longevity [6 marks]

Life insurance companies are keenly interested in predicting how long their customers will live, because their premiums and profitability depend on such numbers. An actuary for one insurance company gathered data from 100 recently deceased male customers. He recorded the age at death of the customer plus the ages at death of his mother and father, the mean ages at death of his grandmothers and the mean ages at death of his grandfathers. These data are recorded in columns 1 to 5 respectively, in file LONGEVITY.xlsx. 

1. Perform a multiple regression analysis on these data.

2. Interpret the coefficient estimates and their signs.

3. Test for the significance of all the independent variable coefficients. (α = 0.05)

4. Is the model likely to be useful in predicting men’s longevity?

5. Are the required conditions satisfied? Justify your answer.

6. Predict the longevity of a man whose parents lived to the age of 70, whose grandmothers averaged 80 years and whose grandfathers averaged 75.

Suppose that in addition to these data, the actuary also recorded whether the man was a smoker (1 = yes, and 0 = no). These data are recorded in column 6 of the same file.

g. Perform a multiple regression analysis on these data.

h. Compare the estimation results produced in part g with those in part a. Describe the differences.

i. Does smoking affect length of life (α = 0.05)? Explain.

QUESTION A5:  Unloading Times [6 marks]

One of the critical factors that determine the success of a catalogue store chain is the availability of products that consumers want to buy. If a store is sold out, future sales to that customer are less likely. Because of this, stores are regularly resupplied by delivery trucks operating from a central warehouse. In an analysis of a chain’s operations, the general manager wanted to determine the factors that affected how long it took to unload delivery trucks. A random sample of 50 deliveries to one store was observed. The times (in minutes) to unload the truck, the total number of boxes and the total weight (in hundreds of kilograms) of the boxes were recorded. The data are recorded in file, TIMES.xlsx.

1. Estimate the multiple regression equation. Interpret the coefficients estimates and their signs.

Further to analyzing the factors that affect the amount of time taken to unload a truck, the manager realised that another variable may affect unloading time: the time of day. He recorded the following codes: 1 = morning; 2 = early afternoon; 3 = late afternoon. 

b Run a regression using the codes for time of day. What is the problem associated with this model specification?

c Create dummy variables to represent time of day. Perform a regression analysis with these new variables.

d Compare the results of the models in parts a and c. Which model fits better? Why?

e Does the time of day affect the time taken to unload?

f Produce predictions for the amount of time needed to unload a truck with 100 boxes of total weight 5000kg during the three times of day.

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