SMUC Multiple Choice
Which of the following is not a logical or relational operator in Python?
/
How many events do we expect in a Poisson interval to obtain the density function of an exponential distribution?
0
What is the mean of the distribution of the error e in a linear regression model?
0
What is the mean of the distribution of the error 𝜺 in a linear regression model?
0
How is "TRUE" coded in Python?
1
What is the total probability of a Uniform distribution?
1
What is the output of this code: np.repeat(np.array([1,2,3,4]),2)
1 1 2 2 3 3 4 4
How can we get help on a particular function in Python?
?function_name
Drawing one pseudo-random uniform variable from the interval [0,1] for a coin toss experiment is...
A Simulation experiment
What is a Dummy Dataset?
A collection of simulated random variables
What is a Monte Carlo simulation?
A computational algorithm that uses random numbers to simulate a wide range of possible outcomes for a particular system or process
What is the interpretation of B1 in a quadratic model?
A location parameter without a specific meaning
What is an input variable in a Monte Carlo simulation?
A variable that affects the behavior of the system or process being modeled
What is the last step in developing a Monte Carlo simulation?
Aggregate the results
In the context of the best subset regression, which criteria can be used to identify the best model among: M0, M1, M2 ...
All the responses are correct
Which of the following is NOT a characteristic of a Monte Carlo simulation?
All the variables in the experiment are discrete
How many conditions can we introduce in a Python program?
As many as we want
How many nested loops can we create in Python?
As many as we want, always trying to reduce the computational cost
What is the keyword we use in Python to avoid an infinite loop?
Break
How does the least squares method define 'best-fit'?
By minimizing the sum of squared errors between the observed values and the values predicted by the model
The concept we use to measure how two variables are linearly dependent on each other is called...
Correlation
What is the first step to perform a monte carlo simulation?
Define the domain of the random variables to be simulated
What is a potential disadvantage of using higher-order polynomials in regression models?
Difficulty in interpreting the parameters compared to linear cases
Which of the following is not a type of Simulation
Direct Simulation
In a cubic model with a single quantitative independent variable x, what is the form of the model?
E(y) = B0 + B1x + B2x^2 + B3x^3
What does a positive slope in a linear regression model imply?
E(y) increases by the amount of B1 for each unit increase in x
A system is a set of related...
Entities or resources
During a simulation study, an instant of time where the state of the system changes is called
Event
Your objective is to simulate covid spread in the IE over 2021. What type of distribution is the most appropriate?
Exponential
If we fix a good seed, the experiment will never be replicated.
False
What property must the variance of the distribution of the error e have for all values of the independent variable x?
Homoscedacity
What property must the variance of the distribution of the error 𝜺 have for all values of the independent variable x?
Homoscedasticity
What more rigorous method than a histogram can we use to see if the pseudo-random numbers have been generated uniformly?
Hypothesis testing
According to the hierarchical principle, if you include an interaction term in a model, you should:
Include all main effects, regardless of significance
If you include a power of order n in your polynomial regression mode, what should you also do?
Include all powers of a smaller order
How should a set of variables be to be considered a simple random sample?
Independent and identically distributed
For the random variable that represents the number of heads obtained by flipping a perfect coin 4 times, we find that
Its variance is 1
Given a Poisson distribution, choose the false statement
Lambda can only take integer values
What is the main difference between linear regression and logistic regression?
Linear regression is used for predicting continuous values, while logistic regression is used for predicting discrete values
Which of the following can be simulated through a static model?
Load capacity of a ship
How can we access the element that is in the second column and third row of a numpy matrix "M"?
M[2,1]
What does the maximum likelihood estimation method do in logistic regression?
Maximizes the likelihood of the observed data under the model
Which method is used to estimate the model coefficients in logistic regression?
Maximum likelihood method
Which of the following is a continuous system?
Money available in an account
What is the relationship between probability and odds?
Odds are the ratio of the probability of an event occurring to the probability of it not occurring
Which of the following is NOT a valid application of logistic regression?
Predicting the selling price of a house based on its size, location and age
Any Simulation Scientific Report should allow the Simulation to be...
Replicated
In a DES, what type of processes do entities flow through?
Sequential processes
In the context of predicting sales based on Youtube and Facebook advertising budget, what would be the interpretation of a significant positive interaction term between Youtube and Facebook?
Spending on Facebook advertising increases the effectiveness of Youtube adverstising on sales
In a system, the collection of variables necessary to describe it at any time point is called
State
In numpy we work with atomic vectors, what does this mean?
That vectors can only store one type of data
What does a confusion matrix evaluate in a logistic regression model?
The accuracy of the model's predictions
In an interaction model y = B0 +B1x1 + B2x2 + B3x1x2, the term (B1 + B3x2) represents:
The change in E(y) for every 1-unit increase in x1, holding x2 fixed
In logistic regression what do the coefficients represent?
The change in the odds that the response variable equals 1 when one of the predictor variables change by one unit
What does the ROC curve represent in the context of logistic regression?
The curve of sensitivity versus 1-specificity
Which of the following is NOT an assumption related to the random error 𝜺 in a linear regression model?
The errors are dependent
How is the logistic regression coefficient B associated with a predictor X interpreter?
The expected change in log odds of having the outcome per unit change in X
In backward stepwise selection, which model does the process begin with?
The full model
In a multiple linear regression model that estimates students´ final grades based on hours of study per week(x1) and the quality of the teacher(x2), what does the interaction term (B3x1x2) represent?
The interaction between hours of study and the teacher quality on final grades
An interaction model is appropriate when:
The linear relationship between y and one independent variable depends on the value of the other independent variable.
What can be inferred about a logistic regression model if its AUC index is close to 0,5?
The model has no class separation capacity
In a confusion matrix, what does True Positive (TP ) represent?
The model predicted a positive outcome, and it was actually positive
Which of the following is true about the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)?
The model with the lowest AIC and BIC values is considered the best
In forward stepwise selection, which model does the process begin with?
The null model
What is the primary difference between simple linear regression and multiple linear regression?
The number of Independent variables used as predictors
What is the interpretation of a positive logistic regression coefficient?
The predictor variable increases the odds of the outcome
What does the e represent in a simple linear regression model?
The random error component
What does the 𝜺 represent in a simple linear regression model?
The random error component
How does the estimated slope for x1 in a positive interaction model change when the value of x2 increases?
The slope increases
What does the B1 represent in a simple linear regression model?
The slope of a line
What does the 𝜷1 represent in a simple linear regression model?
The slope of the line
In a simple linear regression model what does the B0 represent?
The y-intercept of the line
In a simple linear regression model, what does the 𝜷0 represent?
The y-intercept of the line
What is the main reason for using cross-validation in mode selection for linear regression?
To avoid overfitting problems
What is the main goal of model selection in linear regression?
To choose the model that best balances goodness of fit and model complexity
What is the primary purpose of the Akaike Information Criterion (AIC)?
To compare different logistic regression models
What is the main purpose of using R-squared (R2) and adjusted R-squared (adj R2) in linear regression models?
To compare the goodness-of-fit between the models
In the context of logistic regression, what is the purpose of calculating the exponential of the coefficients?
To convert the coefficients to odds ratios
What is the main purpose of using the F-test in linear regression modes?
To determine if a model is significantly better than another nested model
What is the purpose of the Least Squares Method?
To determine the line that minimizes the SSE around it
What is the purpose of the Variation Inflation Factor (VIF) test in multiple linear regression?
To identify multicollinearity between predictor values
What is the purpose of the correlation coefficient (r) in a linear regression model?
To measure the degree of association between the independent and dependent variables
What is the main purpose of using Monte Carlo simulation for inference?
To reduce the uncertainty about a statistical estimate
What is the purpose of using the logit transformation in logistic regression?
To transform the left side of the equation to have the same range as the right side of the equation
If we want to generate random numbers from 1 to 6 to simulate a die we will use a...
Uniform Distribution
An insurance company with 1000 clients has a probability of suffering an accident in one year = 0.005
We model the number of accidents in a year with a Binomial (1000; 0.005)
Simulation is an appropiate tool when...
We want to perform a "what if..." analysis
In a quadratic model, what does the sign of the coefficient of the quadratic term indicate?
Whether the curve is convex (mount shaped) or concave (bowl shaped)
What is the logistic regression model equation?
ln(p/(1-p)) = B0 + B1x
Given a Z standard normal distribution, specify the expected value and the standard desviation:
mu = 0; sigma = 1
What is the best function to simulate a categorical variable?
np.random.choice()
Which function do we use to generate random numbers from a Gaussian distribution?
np.random.normal()
What is the function used in R to generate equally probable pseudo-random numbers?
np.random.uniform()
What function do we use to calculate the density of a specific number in a Uniform distribution?
stats.uniform.pdf()
What are the main properties of the pseudo random numbers?
uniformity and independence
Which of the following codes allows us to access the fourth element of a vector "v"?
v[3]
When do we say that a numerical sequence is statistically random?
when it contains no recognizable patterns or regularities
Which of the following represents a deterministic model?
y = 90+12x
Which of the following is an example of an interaction model relating E(y) to two quantitative independent variables x1 and x2?
y = B0 + B1x1 + B2x2 + B3x1x2 + e
