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What does a high variance indicate?A high variance indicates that values of X have a high probability of being far from the mean values
What is the unit of variance?The variance (sigma^2) is the unit of the random variable X but squared (X [m], sigma^2 [m^2]
How is variance denoted?Var(X), simga_x^2 or sigma^2
What is the unit of standard deviationThe same unit as random variable X (if X is [m], sigma is also [m])
How do you calculate standard deviationsqrt(variance)
What is the symbol for standard deviationSigma
What is a stochastic variable?"It is a function which assigns a real number to every element of the state space. For example a stochastic variable X can denote the amount of heads there are when you throw a coin three times.<br><img src=""paste-0d68e2316e164119fe0a8526a899f47342f6866b.jpg"">"
What is the difference between continuous and discrete stochastic variables? Assume the stochastic variable is XContinuous: X is on a continuous scale - temperature, speed, mass. Basically a continuous line.<br><br>Discrete: X takes a finite or infinite list of values - number of heads in a coin toss or the number of machines that break down over a year. Basically a list of points.
What is a standard deviationIt is a measure of variability of a population or a sample
What is a standard errorThe standard error measures the variability of an estimate such as the variability of the sample mean<br>
What is the formula for standard error?se=sd/sqrt(n) where sd is standard deviation and n is number of samples
What is a quantile? What are some types of quantiles?It defines a particular part of the data set which contains the same fraction of the total population.<br>Quartile - 25% of the population<br>Quintile - 20% of the population<br>Percentiles - 1% of the population
What is a histogram?"A histogram shows frequency distributions. It divides a data set into equal groups (bins) and shows how much data is in each set.<br><img src=""paste-ae0aa63ca5e54ce3cf62f8bfa5574a38d3df577e.jpg"">"
What is a box plot?"A box plot shows how you data is distributed. It
stretches from the interquartile (quartiles of the data) data which is q1(25%) and q3(75%) with the
median splitting the box in two. The box on each side of the median contains the same amount of data points. Whiskers show data points outside og the interquartiles."
How far do the whiskers of a box plot extend?"On each side there are ""whiskers"" which show the min- and max data, provided that they are within 1.5 times of the interquartile range - everything else is considered outliers."
What is a normal distribution?It is a symmatric bell shaped continuous distribution&nbsp;
Which parameters does a normal distribution depend on?The mean mu and the standard deviation sigma
What part of the population is within 1, 2 and 3 standard deviations of the mean of a normal distribution?"1sd ~ 68%<br>2sd ~ 95%<br>3sd ~ 99.7%<br><img src=""paste-501d5e434b001ffd398208ae55b8d6fdefcdf7a2.jpg"">"
What does signam effect in a normal distribution?"The ""flatness"" of the curve"
What is the central limit theorem?It basically states that if you have enough samples then your sample mean will be close to the population mean.
"What is considered ""enough"" samples for the central limit theorem to be accurate?"n ≥ 30
What is the state space?It is the set of all possible outcomes<br>
What is a population?Any complete group with at least on characteristic in common<br>
What is a sample?A sample refers to a smaller (and more manageble) portion of a larger group.
How does one calculate degrees of freedom?n-1 where n i number of samples
What are degrees of freedom?The degrees of freedom are the number of the independent pieces of information available to find the variance
What does covariance measure?The relationship between two variables
What does it mean when a covariance is positive, negative and 0?Positive covariance: Indicates that the variable X tends to be large when the variable Y is large and X tends to be small when Y is small.<br>Negative covariance: X tends to be large when Y is small and vice verca<br>0 Covariance: X and Y are statistically independent
What is a stochastic process?Any process which describes how a random phenomenon changes over time
For a Weibull distribution: What is k and what does it affect?"K is the shape parameter - it determines the shape of the distribution<br><img src=""paste-2d0614c7d76c5510e392c29572f29df871fbeb9b.jpg"">"
For a Weibull distribution: What is lambda and what does it affect?Lambda is the scale parameter - it scales the x axis
What a confidence interval for a parameter?"It is the probability that a population parameter falls between two set values<br><img alt=""What are Confidence Intervals? - Simply Psychology"" src=""confidence-interval.jpg"">"
What is the point of using a normal QQ plot?We plot a line which follows a normal distribution. Then we plot the points of our data to see how it follows the normal distribution
What is a confidence intervalAn interval around a point estimate in which we are confident (to a degree - usually a percentage) that the population parameter lies
What are possible values of dummy variables and what are they used for?Dummy variables either have a value of 0 or 1. They are essentially used to assign an observation to a reference group&nbsp;
"What is ""anova"" used for?"Anova is used to compare two models to see if the more complex model is significantly better than the less complex model.
"When using ""anova"" when can we say that a model is significantly better than the alternative?"Is the p value is below 0.05, the more complex is considered significantly better.
What is AIC? What does its output suggest?"""Akaike’s Information Criterion"" - Essentially a balance between simplicity and a good fit for a model. The lower an AIC is for a model fit, the better the fit."
What is the idea behind an Auto-regressive (AR(1)) model?If there is a significant auto-correlation at lag 1, then the previous value x_(t-1) can be used to predict the current value x_t
What is a moving average (MA) model used for?Predicting future values based on past errors
What does an ARMA model do?Combines regression models to obtain a stochastic process which is influenced by exogenous variables
What are exogenous variables?A variable, say y_t, that affects the behaviour of x_t
How is a higher order auto-regressive model different from a first order one?"More lagged terms are added to explain the current value<br><br>AR(1) process:<br><img src=""paste-b702529b586d0c3079868d9bcf8d96f741644fc7.jpg""><br><br>AR(P) process:<br><img src=""paste-c6e336ad9a2164d1b9846c30e85f4da94960eb6d.jpg"">"
What is white noise?The simplest stochastic process. X_t are independent and identically distributed variables
Is white noise second order stationary?"Yes - the variance function&nbsp;σ^2
(t) = σ^2
is the same constant for all t"
What is the mean of white noise?It is 0
How is white noise denoted?w_t
What is random walk?"A random process which describes a path of random steps in succession. It has a tendency to ""wander off""<br><img src=""paste-2bd589d1dca161c63ad7a79bc29ba30f78fb8279.jpg"">"
Is random walk stationary?"No - the variance depends on the time t&nbsp;<img src=""paste-ee40f539cb90cd87a69dbf2c10d93d572483a087.jpg""><br>"
What is the mean of random walk?mu(t) = 0
What does a t value express?It is a measure of how many standard deviations our coffiecient estimate is away from the mean (of the t distribution)
What does a p value describe?"The p value of a model relates to the probability of observing any value equal or larger
than t. A small p-value indicates that it is unlikely we will observe a
relationship between the predictor (speed) and response (dist) variables due to chance."
When can we say that a correlation is statistically significant?When its p value is above 5% or 0.05