Problem Set 2: Linear Regression Analysis

Research Scenario: A social psychologist is interested in whether the number of days spent in a refugee camp predicts trauma levels in recently resettled refugees. He interviews 17 refugees to determine how many days they spent in a refugee camp before being resettled, then administers the Harvard Trauma Questionnaire Part IV (HTQ Part 4), where a higher score indicates higher levels of trauma (Mollica et al., 1992). He compiles the information in the table below.

Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether days in a refugee camp predict HTQ-4 scores. Create a scatterplot with a regression line to show the relationship between the variables.

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your scatterplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts; Graph = 5 pts)

Problem Set 2: Linear Regression Analysis

Research Scenario: A social psychologist is interested in whether the number of days spent in a refugee camp predicts trauma levels in recently resettled refugees. He interviews 17 refugees to determine how many days they spent in a refugee camp before being resettled, then administers the Harvard Trauma Questionnaire Part IV (HTQ Part 4), where a higher score indicates higher levels of trauma (Mollica et al., 1992). He compiles the information in the table below.

Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether days in a refugee camp predict HTQ-4 scores. Create a scatterplot with a regression line to show the relationship between the variables.

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your scatterplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts; Graph = 5 pts)

Suppose 1% of the population of Toronto has been infected with SARS-CoV-2 at some point (call the corresponding proportion, 0.01, the prevalence of the virus). There are now antibody tests available for SARS-CoV-2 to detect whether someone has ever been infected. However, like any test, these tests are not perfect and are subject to error at some rate.

Also suppose that, when someone has been infected, the test correctly comes up positive 98% of the time, comes up negative 1.7% of the time, and comes up inconclusive in the remaining 0.3% of cases. Also suppose that when someone has not been infected, the test correctly comes up negative 99% of the time, positive 0.8% of the time, and inconclusive 0.2% of the time.

Let ?D be the event that a randomly selected person in Toronto has truly been infected (?D for disease). Thus, ??Dc is the event that the person has never been infected. Let ++ be the event that a test comes up positive, and – the event it comes up negative. Use ?O for inconclusive.

Draw a probability tree to depict the relationship between these events (see Lecture 7). Use the tree to compute ?(?|+)P(D|+), the probability that someone has been infected conditional on getting a positive test result. What does this result mean in words and why might it be surprising (1-2 sentences)?

The sales and finance team of a car company is evaluating a new proposed luxury model of its
brand that will require an investment of $1Billion in a new machine for car interior decoration.
Demand for the company’s car is expected to begin at 100,000 units in year 1, with 10% annual
growth thereafter. Production cost will be $35,000 per unit in the first year, and increase by a rate
of either 3% or 5% per year as a result of wage increase. Selling price will start at $37,000 and
increase by 4% of the production cost. The model will be phased out at the end of year 10. In
addition, 0.3%, 2% and 1.5% of before tax profit per year will be spent on social corporate
responsibility, commercial (including promotions) and recalls respectively. Assume taxes will be
30% of yearly profit and that inflation will remain at 0% per year throughout the 10 year of
production. Also assume interest rate is expected to be 3% per year in the first 5 years and 5% in
the last 5 years.
a. Based on present worth analysis, is the proposed investment profitable if production cost
increases by a rate of 3% per year as a result of wage increase? Justify your answer.
b. Based on present worth analysis, is the proposed investment profitable if production cost
increases by a rate of 5% per year as a result of wage increase? Justify your answer.

RS p.1.c. manufactures domestic food mixers. It is investigating whether or not to accept a three-year contract to make a new model for sale through a supermarket chain. The contract uses skilled labour which cannot be increased above that currently available and RS p.1.c. will receive a fixed price of £42 per mixer for all the mixers it can produce in the three-year period. The following estimates have been made:

Capital investment £50000 payable now, with nil scrap value.

Additional overhead £25000 per annum.

Materials £30 per mixer Labour £6 per hour.

The factory manager knows from experience of similar machines that there will be a learning effect for labour. He estimates that this will take the form:

y = ax^-0.3

where y = average labour hours per unit

a = labour hours for first unit

x = cumulative production

He estimates that the first mixer will take 10 hours to produce and that the fixed amount of labour available will enable 5000 mixers to be produced in the first year. Apart from the capital investment, all cash flows can be assumed to arise at year ends. The company has a cost of capital of 15%. You are required

(a) to calculate the NPV of the proposed contract

(b) to state what other factors need to be considered before a final decision is made.

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6.6 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $643,000. The firm believes that working capital at each date must be maintained at a level of 15% of next year’s forecast sales. The firm estimates production costs equal to $1.90 per trap and believes that the traps can be sold for $6 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 12%. Use the MACRS depreciation schedule.

A) . What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

B) By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

An person has applied for positions at Company A, Company B and Company C. The probability of obtaining an offer from Company A is 0.3, from Company B is 0.6 and from Company C is 0.8. Assume that the three job offers are independent.

A)What is the probability that the person will receive a job offer from ALL three companies?

B)What is the probability that the person will receive a job offer from Company A only ?

C)What is the probability that the person will receive job offer from Company B only ?

D)What is the probability that the person will receive job offer from Company C only ?

E)What is the probability that the person will receive a job offer from exact one company (either A, B or C)?

F)What is the probability that the person will receive a job offers from Company A and B but not C?

G)What is the probability that the person will receive a job offers from Company A and C but not B?

H)What is the probability that the person will receive a job offers from Company B and C but not A?

I)What is the probability that the person will receive a job offers from exactly two companies?

K)What is the probability that the person will not receive any job offers?

L)What is the probability that the person will receive at least one job offer (i.e. either 1 or more)?

(PLZ ANSWER ASAP)

A Cessna 172 has the following characteristics: Wingspan: 36’ 1” Wing Area: 174 ft2 Normal Gross Weight: 2,450 lb Fuel Capacity: 54 gal of aviation gasoline Power Plant: 1 × Lycoming IO–360–L2A piston engine, 180 hp Specific Fuel Consumption: 0.3 lb/hp-h Parasite drag coefficient: CD,0 = 0.037 Oswald efficiency factor: e = 0.72 Propeller efficiency: 0.8 #Passengers: 3 (+1 pilot)

(a) Produce a plot showing the power required vs. velocity of the aircraft. Label the axes clearly. [Use Excel or a programming language of your choice]

(b) Produce a plot showing the L/D ratio vs. velocity. Label the axes clearly. [Use Excel or a programming language of your choice]

(c) What is the maximum velocity at sea level?

(d) What is the minimum flight velocity at sea level?

(e) What is the maximum velocity at 5,000 ft?

(f) What is the maximum rate of climb?

(g) What is the service ceiling?

(h) How long does it take to get to the service ceiling?

(i) If you run out of fuel at an altitude of 5,000 ft, how far can the plane glide?

(j) What is the maximum range?

(k) What is the range at maximum velocity?

(l) What is the maximum endurance?

(m) What distance is required for takeoff?

(n) What distance is required for landing?

Jason Scott has applied for a mortgage to purchase a house, and he will go to settlement in two months. His loan can be locked in now at the current market interest rate of 7% and a cost of $1,000. He also has the option of waiting one month and locking in the rate available at that time at a cost of $500. Finally, he can choose to accept the market rate available at settlement in two months at no cost. Assume that interest rates will either increase by 0.5% (0.3 probability), remain unchanged (0.5 probability), or decrease by 0.5% (0.2 probability) at the end one month.

Rates can also increase, remain unchanged, or decrease by another 0.5% at the end on the second month. If rates increase after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.5, 0.25, and 0.25, respectively. If rates remain unchanged after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.25, 0.5, and 0.25, respectively. If rates decrease after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.25, 0.25, and 0.5, respectively.

Assuming that Jason will stay in the house for 5 years, each 0.5% increase in the interest rate of his mortgage will cost him $2,400. Each 0.5% decrease in the rate will likewise save him $2,400. What strategy would you recommend?

How do you set this up in excel?