Reference no: EM132253170

Questions -

Question 1 - While working on the Breakfast Foods case, one team developed two models for predicting the actual price of wheat. FSBsrats outputs for both models are attached.

(a) Use the provided output (and coefficient estimates there) to write down the equation of the best fit line for the "Two-Variable" regression (Model 2). Furthermore, what is your best guess for the distribution of the error term of Model 2?

(b) If we use the "Three-Variable" regression (Model 1) to forecast Actual_Price, can the standard error of the forecast be smaller than 3.5? Explain your answer.

(c) Use the "Two-Variable" regression (Model 2) to provide an estimate of the probability that Actual_Price will be below $310 when Rick's forecast is $290 and Harry's forecast is $350.

(d) Use the "Two-Variable" regression (Model 2) to provide a 95% confidence interval for the change in Actual_Price when Rick_Fcst decreases by $2 and Harty_Fcst remains unchanged.

Question 2 - Pino manages a small rent-a-car company on a Mediterranean island. The company rents two types of cars: small can and family cars. The profit of renting a small car to a customer is €50 plus €3/km (50 Euro, plus 3 Euro per every kilometer driven), while the profit of renting a family car to a customer is €60 plus €2/km.

Pino asked Rahul, the manager of the small car fleet, to gather data on kilometers driven from small car rentals. Rahul reported to Pino that the average km driven for small car rentals in the sample was 210km, with the standard error of 4km. For family car rentals, Pino obtained a data set of 5,184 family car rentals and computed the sample mean of 315km and the sample standard deviation of 201.6km.

(a) Based on the observed sample data, how confident can you be that the average number of kilometers driven on a family car rental is at least 100km larger than the average number of kilometers driven on a small car rental?

(b) Pino needs to decide whether to add 10 family can or 10 small can to the car fleet. Pino will receive a bonus if the expected profit from renting these 10 additional can will be at least €7000. He computed 95% confidence intervals for the expected profit from 10 family car rentals ([6788, 7012], with Point Estimate = 6900 and SE = 56) and for 10 small car rentals ([6560, 7040], with Point Estimate=6800 and SE=120). If Pino wants to maximize his chance of receiving a bonus, should he add 10 family cars or 10 small can to the fleet? Why?

Question 3 - Speculate is an internet trading company. The company is worried about the continual market slide; it seems to have resulted in a significant decline in both the total number of trades Speculate executes and the number of customers who actively trade on Speculate.

(a) According to the results of a recent survey among 150 randomly selected Speculate customers, the average return on $1 invested among the 150 respondents was 96 cents (they lost 4 cents) with a sample variance of (25 cents)². Based on the survey results, how confident can you be that Speculete customers are losing money on average?

(b) A sizeable proportion of Speculate customers seem to be day-traders (i.e.. speculators in volatile stocks that close their positions at the end of every trading day). Speculate estimates that at the end of the day, the return on $1 invested in day-trading is normally distributed. Speculate 's trading records suggest that, on average, $1 invested in day-trading is worth only 95 cents at the end of the day (i.e.. day-traders lose money as a group even though there might be some individual day-traders who make a fortune). The records also suggest a 45% chance that a $1 day-trading investment will turn out profitable at the end of the day. Using Speculate records and estimates, find the standard deviation of the return at the end of the day on $1 invested in day-trading.

(c) During any given trading hour, the distribution of the number of complaints related to on-line access problems when placing a trade request has a mode of 0, a median of 2, and an expected value of 3.4. A sample indicating the number of complaints for each of 400 randomly selected one-hour trading intervals has been collected. What is the probability that the observed sample mean is less than 3.4?

Circle all correct answers:

• 0.5 because observing something below average always has probability 0.5.
• 0.5 because the probability of observing a value of a normal random variable that is below average is 0.5.
• 0.588 = 2/(3.4) because the median is two and the average is 3.4.
• 0.07 = (3.4-2)/20 since n=400. (Note that the square root of 400 is 20.)
• 0.93 = 1-0.07 = 1- (3.4-2)/20 since n=400. (Note that the square root of 400 is 20.)
• All the above are wrong, and here is the correct answer (explain):

Question 4 - Bernie is investing in only two stocks: T3G, a telecom giant, and SSB, the bank he used to work for. He believes that at the end of the year, the return on $1 invested in T3G is best described by a random variable T with mean μ_T and standard deviation σ_T > 0, and the return on $1 invested in SSB is best described by a random variable S with mean μ_S and standard deviation σ_S > 0. Bernie invests the same amount in each of the two stocks and would like to exit the market at the end of the year. Let

P = (1/2) S + (1/2) T

denote the random variable describing the return on $1 invested in Bernie's portfolio at the end of the year, and let μ_P and σ_P denote the mean and the standard deviation of P, respectively.

In each of the questions below, circle only the correct statements.

(i) If S and T are positively correlated, then

• μ_P < (μ_S+μ_T)/2
• μ_P = (μ_S+μ_T)/2
• μ_P > (μ_S+μ_T)/2

(ii) If S and T are negatively correlated, then

(σ_P)² < (1/4)(σ_S)²+(1/4)(σ_T)²

(σ_P)² = (1/4)(σ_S)²+(1/4)(σ_T)²

(σ_P)² > (1/4)(σ_S)²+(1/4)(σ_T)²

(iii) If σ_P = (σ_S+σ_T)/2, then

• correlation between S and T, ρ_ST = -1.
• correlation between S and T, ρ_ST = -0.25.
• S and T are independent.
• covariance of S and T is zero.
• correlation between S and T, ρ_ST = 0.5.
• correlation between S and T, ρ_ST = 1.

Question 5 - Three multiple regressions were run on data from 52 commercial rental real estate properties in the San Fernando valley of Los Angeles, and the outputs (MODEL A, MODEL B, and MODEL C) are attached.

(a) Consider MODEL A (TotalRent, 5 Variables). Based on the provided FSBstats output, list all independent variables that are significant at the 90% confidence level or more. (List all such variables, if any. No explanation needed or credited.)

(b) If data for one more variable were collected and if this new variable were added to MODEL B, then in the new regression:

i) The slope of that new variable would be significant at a 95% confidence level.

ii) The intercept coefficient would become significant at a 95% confidence level.

iii) The adjusted R² would decrease.

iv) R² would not decrease.

v) R² could increase to 1.

vi) None of the above.

Select all that apply and justify your choices.

(c) If 12 more data points were added to the sample, then in MODEL B:

i) The 12^th autocorrelation would be significant at a 95% confidence level.

ii) The intercept coefficient would stay insignificant at a 95% confidence level.

iii) The adjusted R² would increase.

iv) R² would not increase.

v) R² could increase to 1.

vi) None of the above.

Select all that apply and justify your choices.

(d) Consider MODEL A (TotalRent, 5 Variables) and MODEL B (TotalRent, 3 variables). Which of the following statements are true/false? (No explanation needed.)

MODEL A is better than MODEL B because it has a higher adjusted R-squared and smaller Standard Error of Regression. TRUE/FALSE

MODEL B could be better than MODEL A for predictive purposes because, at a 95% confidence level, forecasts using MODEL B could be more precise than corresponding forecasts using MODEL A. TRUE/FALSE

MODEL A is better than MODEL B because the largest p-value in MODEL A is only 0.109, while the largest p-value in MODEL B is 0.480. TRUE/FALSE

MODEL B is better than MODEL A because it has a smaller number of independent variables and thus more degrees of freedom. TRUE/FALSE

Neither of the two models (MODEL A or MODEL B) is useful for forecasting since the Standard Error of Regression is huge in both models. TRUE/FALSE

Neither of the two models (MODEL A or MODEL B) is useful for forecasting since the intercept coefficient is negative in both models. TRUE/FALSE

Every forecast from MODEL A will have a Standard Error of Forecast smaller than 1604.871. TRUE/FALSE

Every forecast from MODEL B (including the one presented in the output) will have the Standard Error of Forecast higher than the Standard Error of Regression for MODEL A. TRUE/FALSE

InvDist coefficient in MODEL A has the largest p-value because it has the largest coefficient value and the largest standard error among all coefficient estimates in MODEL A. TRUE/FALSE

SquareFeet coefficient in MODEL B has the smallest p-value because the absolute value of its t-stat is the largest among all four t-stats reported in MODEL B. TRUE/FALSE

(e) Winston owns a 20.000 ft² building with 7,000 ft² of office space and 100 parking spaces. Use MODEL C (Rent/ft², 2 Variables) to give a point estimate for the total monthly rent (i.e., in $ for the whole building) for Winston's building.

(f) Use MODEL C (Rent/ft², 2 Variables) to construct a 95% confidence interval for the predicted monthly rent per ft² of a warehouse with no office space and no on-site parking spaces.

(g) Use MODEL C (Rent/ft², 2 Variables) to construct a 95% confidence interval for the average monthly rent per ft² among warehouses with no office space and no on-site parking space.

(h) A real estate agent relates a story about two almost identical real estate properties with the only difference being that one has 40% of the area devoted to the office space and the other has no office space at all. The agent claims that the property without any office space has a higher monthly rental rate than the one with 40% of square footage devoted to the office space. Based on three regression models provided, should you be surprised? Explain your reasoning.

(i) Out of 52 randomly selected commercial real-estate properties, 30 have less than 25% of area devoted to the office space. How confident can you be that at least half of the commercial real-estate properties in San Fernando Valley have less than 25% of the area devoted to office space?

(j) Vince is thinking about buying a 15,000 square feet building which has 5,000 square feet of office space and which has 50 parking spaces. Use model B to find the probability he will make a profit on this investment if his mortgage payments are equal to $7,548.74 per month.

Attachment:- Assignment File.rar