## All Weeks Fundamentals of Quantitative Modeling Coursera Quiz Answers

### Fundamentals of Quantitative Modeling Week 1 Quiz Answers

#### Quiz 1: Module 1: Introduction to Models Quiz

Q1. Which of the following features is typically NOT associated with a quantitative model for a business process?

**A 100% accurate representation of the business process**- Assumptions
- A formal description of a business process
- Mathematical equations

Q2. For which activity(ies) might you use a quantitative model?

- (i) Forecasting
- (ii) Targeting
- (iii) Optimization

- (i)
**(i), (ii), and (iii)**- (ii) and (iii)
- (i) and (ii)

Q3. Which of the following activities is typically NOT a part of the modeling process?

- Model formulation
- Validation
**Creating a model, so that the output always agrees with our prior expectations**- Sensitivity analysis

Q4. If a model gives a different output even when the inputs are the same, then what sort of model **must** it be?

- Deterministic
**Probabilistic**- Dynamic
- Discrete

Q5. From a modeling perspective, what is the key difference between a digital and an analog thermometer?

- The digital thermometer always provides a more accurate reading of the temperature
**The digital thermometer provides a discrete reading of the temperature, whereas the analog provides a continuous one**- There is no difference, because they will always provide identical readings of temperature
- The digital thermometer provides a continuous reading of temperature, whereas the analog provides a discrete one

Q6. In the model y=3 e^(0.02 t) , where t is measured in months and y measures the number of customers in thousands, what is the best interpretation of the coefficient 0.02?

- Two-thousand extra customers are added every month
**The monthly customer growth rate is approximately 2%**- For every 1% increase in months there will be a 2% increase in customers
- The annual customer growth rate is approximately 2%

Q7. What is the ** defining** characteristic of the

**model y =3+4 x, where x is the number of units produced and y is the time in hours it takes to produce them?**

*linear*- When x goes from 4 to 5, the change in y is larger than when x goes from 40 to 41
**The rate of change in y is constant at 4 hours per unit**- If x increases by 1% then y will increase by 4%.
- The model has a set-up time of 3 hours

Q8. For which of the following business processes is a log function particularly useful in modeling the output?

- A process that exhibits a constant growth rate
**A process that exhibits diminishing returns to scale**- A process that is increasing at a constant rate
- A process that exhibits seasonality

Q9. If you wanted to model a business process that looked like the graph below, then which modeling function would you suggest?

- Linear
- Log
- Any of these
**Exponential**

Q10. When would you choose to use a dynamic model for a business process?

**When there is specific interest in the state to state transitions of the process**- When there is more than one input to the model
- When all of the inputs are random variables
- When there is considerable uncertainty as to what the inputs should be

### Fundamentals of Quantitative Modeling Week 2 Quiz Answers

#### Quiz 1: Module 2: Linear Models and Optimization Quiz

Q1. Which of the following features is a defining aspect of a deterministic model?

**There is no randomness in the model**- It always uses discrete input values
- It only uses linear functions
- It cannot be used as a basis for a subsequent optimization

Q2. Total costs at a company have been modeled as TC = 100 + 12 q, where TC stands for total cost in thousands of USD and q stands for quantity produced, again measured in thousands. What type of function is this?

**Linear**- Power
- Exponential
- Log

Q3. In the model described in Q2, what is the best interpretation of the coefficient 100?

- The elasticity of cost respect to quantity is 100
- Fixed costs are 100 USD
**Fixed costs are 100,000 USD**- The variable costs are 100 USD

Q4. Which of the following modeling functions describes the graph below?

- Cost = 2.5q
**Cost = 25 + 2.5q**- Cost = 25 + 2.5 log(q)
- Cost = 25 + 25q

Q5. A website is increasing its user base by 10% each month. If it has 10,000 users now (t = 0), then how many users does it expect six months from now (t = 6)? Use a discrete model for the growth process.

- 16,105
- 16,000
**17,716**- 18,221

Q6. The number of new domestic wind turbine generators installed each year in a particular country has been forecast to increase at a constant multiplicative rate of 15% per annum for the foreseeable future. This year (t = 0) 100 new generators were installed. What is the total number of new generators including this year’s, that would have been installed within the next ten years (that is up to and including year t = 9)? Use a discrete model for the growth process.

- 2030
**235**- 1679
- 900

Q7. What is the difference between compound interest and simple interest?

- Compound interest rates can only be used if the interest accrues exactly once a year whereas simple interest can be applied multiple times during a year
- The terms are in fact synonyms
**Compound interest means that any prior interest itself earns interest, whereas simple interest is only applied to the principal investment**- Compound interest is applied more often than simple interest

Q8. Using a discount rate of 5%, what is the present value of an investment that provides a lump sum payment of $10,000 in 4 years?

- 8000
**8227**- 10,000
- 12,155

Q9. The number of users of a cloud based storage service is projected to grow according to the growth model: U_t=1,000,000 e^(0.05 t). What is the best interpretation of the value 1,000,000 in this equation?

- It represents the monthly growth rate
- It represents the annual growth rate
- It represents the number of users that they will have in a year’s time
**It represents the current number of users. That is, at time t = 0**

Q10. Consider the demand equation q=20,000 p^(-1.4). If the cost of production is constant at $0.50 per unit then what is the optimal price to maximize profit?

- $1.40
**$1.75**- $0.29
- $0.50

### Fundamentals of Quantitative Modeling Week 3 Quiz Answers

#### Quiz 1: Module 3: Probabilistic Models Quiz

Q1. Which of the following characteristics implies that a quantitative model is probabilistic in nature?

- The fact that it uses an exponential function
- The fact that it measures time in discrete steps
- The fact that it is based on theory rather than data
**The fact that it uses random variables**

Q2. What essential information can a probabilistic model provide, that a deterministic model can’t?

- It can deal with larger amounts of data
- It can provide a more accurate measure of the output
**It can include a range of uncertainty for the model output**- It can be used with both discrete and continuous variables

Q3. Monte Carlo simulation models incorporate uncertainty in what manner?

- They incorporate uncertainty by forcing all random variables in the model to come from a Normal distribution
- Monte Carlo simulations do not in fact incorporate uncertainty
- They allow the analyst to generate any random outcome that they want to see
**They generate a range of inputs for the model using random variables drawn from probability distributions**

Q4. If you wanted to model an outcome variable that is defined as whether or not someone will buy a new car within the next 12 months, then what type of random variable would you use to capture this outcome?

**A discrete random variable**- This future outcome is not in fact random and should be modeled in a deterministic fashion
- A continuous random variable
- Either continuous or discrete, it doesn’t matter

Q5. A Bernoulli random variable, representing whether or not the stock market goes up or down tomorrow (assume that the market cannot be unchanged), has an “up” probability of 0.6 and a “down” probability of 0.4. What is the standard deviation of this random variable?

- 0.4
- 0.24
**0.49**- 0.6

Q6. Using the same probability as described in 5, and assuming that moves in the market are independent from day to day, then what is the probability that the market goes up on exactly 2 of the next 4 days?

- 0.5000
- 0.0576
- 0.7776
**0.3456**

Q7. For which of the following random variables would the use of a Normal distribution as a model be a clear error?

- The daily percentage change on a stock
**The number of houses that an individual owns**- The number of minutes that a battery lasts in a cell phone
- Student test scores on an exam

Q8. A snow tire manufacturer believes that a typical set of snow tires lasts on average for 30,000 miles. They also believe that 95% of drivers get between 20,000 and 40,000 miles of use from the tires. What value of σ, the standard deviation, would be needed to make the information above approximately consistent with a Normal distribution model for tire wear? You should use the Empirical Rule to answer this.

- 10,000
- 3,333
**5,000**- 20,000

Q9. Assuming that a Normal distribution model is reasonable for the tire wear, what is the approximate probability that a randomly drawn driver gets more than 25,000 miles of use from their tires? Use the value for the mean and standard deviation from Q8.

- 0.16
**0.84**- 0.95
- 0.5

Q10. If you had two variables, the weight of a car measured in pounds and the fuel economy measured in miles per gallon, then which of the following quantitative modeling methodologies would be preferred for modeling fuel economy as a function of weight?

- A probability tree
- A Markov chain
- A Monte Carlo Simulation
**A regression model**

### Fundamentals of Quantitative Modeling Week 4 Quiz Answers

#### Quiz 1: Module 4: Regression Models Quiz

Q1. What is the difference between a simple regression model and a multiple regression model?

- There isn’t one. The two terms are equivalent
- A simple regression model can handle only limited amounts of data whereas a multiple regression model can handle large data sets
**A simple regression model has a single predictor whereas a multiple regression model has potentially many**- A simple regression is appropriate for a dichotomous outcome variable, whereas a multiple regression model should be used with a continuous outcome

Q2. A simple regression models which function of the outcome variable (Y)?

- It models the variance of the outcome as a function of X
- It models the standard deviation of the outcome as a function of X
- It models the median of the outcome
**It models the mean of the outcome as a function of X**

Q3. If the simple regression for the expected price (in US$) of a diamond given its weight (in carats) is modeled as E(Price │ Weight) = -260 + 3721 ⨯Weight , then what is the expected price of a diamond that weighs 0.2 of a carat?

- 1004.20
- 744.20
**484.20**- -259.80

Q4. If two variables have a correlation of -1, then what do you know about them?

- They may or may not have a strong linear association
- They have no linear association
- They have a perfect positive linear association
**They have a perfect negative linear association**

Q5. You can NOT use a regression for which of the following activities?

- Forecasting new observations
- Identifying unusual data points
**You can in fact use a regression model for all of these**- Measuring the proportion of variability in the outcome variable explained by the predictor variables

Q6. A simple regression equation decomposes the observed data into two parts: the fitted values and the residuals. What is the interpretation of a residual?

**The vertical distance from a point to the fitted regression line**- The intercept of the regression line
- The horizontal distance from a point to the fitted regression line
- The squared vertical distance from a point to the fitted regression line

Q7. Given the fitted the regression equation of E(Price │ Weight) =-260 + 3721 ⨯ Weight and an RMSE from the regression of 32, then which of the following is the approximate 95% prediction interval for the price of a diamond that weighs 0.2 carats? Assume that the residuals are Normally distributed and that the prediction is within the range of the data that was used to fit the model.

- (3397,3525)
**(420.2, 548.2)**- (680.2, 808.2)
- (452.2, 516.2)

Q8. In the regression demand equation E(log〖(Sales) | Price))=11.015 -2.442 log(Price)〗, at a price of $1, what is the expected value of sales? The log here, is the natural log.

**60,779**- 11
- 1
- 5,287

Q9. What characteristic of the outcome variable (Y) suggests that a logistic regression is a suitable methodology?

- When the outcome is a continuous variable
**When the outcome is a dichotomous variable**- When the outcome is always positive
- When the outcome variable has a large variance

Q10. If, in a multiple regression of the price of a diamond against the two predictor variables, weight and color, the R^{2 }of the regression was 0.985, then which of the following is the best interpretation of this value?

**98.5% of the variation in price is explained by weight and color**- The correlation between price and weight is 0.985
- None of these are true
- The correlation between weight and color is 0.985

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