Introduction to Random Motors Project

Imagine you are the Lead Business Analyst atRandom Motors, an automobile conglomerate that manufactures cars across a large range of price points. Given the scale of your firm, you have different brands for different consumer segments.

For the price-conscious working-class consumers, Random Motors manufactures cars under the brandRocinante.The various models of Rocinante fall in the range of5-10 lakh.The brand is known for cars that arevalue for money and very attractive mileage.

For the consumers willing to purchase a luxury car, Random Motors operates under the brandMarengo.Marengo models fall in the range of30-60 lakh.They are considered sports cars and havehigh horsepower and top speed.

Every time Random Motors launches a new model, it advertises the model's specifications, such as price, mileage, and top speed, because consumers usually take these factors into account before purchasing cars.

Suppose your chief engineer has recently come up with two new models:Rocinante36 and Marengo32.He promises that they will outperform the existing competitors in the market.

Rocinante36is priced at7 lakhand has been designed to deliver a mileage of22 km/litreand a top speed of140 km/hr.

Marengo32is priced at41 lakhand has been designed to deliver a mileage of15 km/litreand a top speed of210 km/hr.

The chief engineer has built 20 prototypes of each of the two models to check if the cars are performing as per the desired specifications. If the cars are performing better than expected, then the engineer wants to revise the specifications. However, if they are performing worse than expected, then it is an indication that more investment is needed in the design to improve their performance.

The test drive results for the 20 prototypes of each of the two models are provided in the file titledData Exhibit 1.During the test, the mileage and the top speed is recorded for each of the prototypes. The data will be used for performing hypothesis testing for the claims made on the specifications.

Additionally, the chief engineer reported that the cost of manufacturing the Rocinante36 model would be6 lakh per carand that of the Marengo32 model would be33 lakh per car, including all the overhead expenses. Given the business scenario, you need to invest the total manufacturing cost upfront. The manufacturing cost will be recovered slowly by the next financial year as sales start happening. These details are summarised in the table given below.

Specifications Rocinante36 Marengo32

Price 7 lakh 41 lakh

Manufacturing cost 6 lakh 33 lakh

Mileage 22 km/litre 15 km/litre

Top speed 140 km/hr 210 km/hr

SpecificationsRocinante36Marengo32Price7 lakh41 lakhManufacturing cost6 lakh33 lakhMileage22 km/litre15 km/litreTop speed140 km/hr210 km/hr

Currently, the company hasenough cash reserves to invest in only one model.Therefore, as the Lead Business Analyst, you need to carefully choose the right model and decide the number of cars that you want to produce. Since you believe in making data-based decisions, you ask your team to provide you with the sales data of all the past models released under the brands Rocinante and Marengo. The sales data is provided in the file titledData Exhibit 2.

Q-1)Formulate the null and alternative hypotheses for mileage and top speed to check whether the new models are performing as per the desired design specifications.

Q-2)In order to comment on whether or not the design specifications are being matched, perform relevant hypothesis tests and calculate the p-values for each model. What will you conclude? Assume that you are performing the tests at a 95% confidence level.

Q-3)You have already learnt about the possible errors that might result from hypothesis tests. Which type of error is more expensive for Random Motors, and why? Assume that you need to refund the money to all your customers if your cars do not deliver the promised specifications.

Q-4)Develop a regression equation for each model at a 95% confidence level. Using the regression equation, predict the sales of the two models. State the hypothesis assumption for the overall test and individual variables.

Q-5)Based on the sales prediction, calculate the overall projected profit for the Rocinante36 and Marengo32 models, respectively?

Q-6)Your company wishes to invest only in the model that can generate high overall profits. In which of the two models, Rocinante36 and Marengo32, should your company invest?

Q-7)You must have developed the regression equation for both the models, Rocinante36 and Marengo32. Suppose you increase the price of Rocinante36 and Marengo32 by 1 lakh each. Which of the two models will have to seea higher impact on sales numbers? Provide proper logic for your answer. (Note: You can assume that all the other specifications, such as mileage and top speed, are the same for both models.)

Q-8)After developing the regression equation for both the models (Rocinante36 and Marengo32), if you analyse the p-values for the coefficients in the regression results, you will notice that some of the regression variables (top speed, mileage and price) are insignificant. Drop the insignificant regression variables and rebuild the regression model using only significant variables. Compare the adjusted R-squared value for both the new and the old regression models. Do you notice any change in the adjusted R-squared value? If yes, explain the reason for the change.