Variance vs Covariance vs Correlation correct answers The variance refers to the spread of the data set — how far apart the numbers are in relation to the mean, for instance.
Var(x) =Sum of squared errors (deviations) / Total number of observations
Covariance is a measure of how changes in...
Econometrics || A+ Guaranteed.
Variance vs Covariance vs Correlation correct answers The variance refers to the spread of the
data set — how far apart the numbers are in relation to the mean, for instance.
Var(x) =Sum of squared errors (deviations) / Total number of observations
Covariance is a measure of how changes in one variable are associated with changes in a second
variable. Specifically, covariance measures the degree to which two variables are linearly
associated. You only care about positive or negative covariance you don't really care about the
number all it really tells you is if it is upward sloping or downward sloping
The problem with covariances is that they are hard to compare: when you calculate the
covariance of a set of heights and weights, as expressed in (respectively) meters and kilograms,
you will get a different covariance from when you do it in other units
Cov(x,y) =(Sum of (xt-xmean) x (yt-ymean)) x P(x,y)
Correlation is a scaled version of covariance that takes on values in [−1,1] with a correlation of
±1 indicating perfect linear association and 00 indicating no linear relationship. This scaling
makes correlation invariant to changes in scale of the original variables
=Cov(x,y)/square root of Var(x) x square root of Var(y)
Standard deviation is square root of Var(x)
Discrete Random Variable correct answers A random variable (a variable that is associated with
an outcome of a random process) that can only take on a countable number of discrete values
Continuous Random Variable correct answers can take on a continuous range of values
Expected Value correct answers Mean(random variable)= multiply each value by the value's
probability and sum it all up
Variance of random variable correct answers variance(v)= sum of (squared deviations of x from
the expected value for x (mean)) x each probability of x
P and Variance of P correct answers p is the expected value and p(1-p)/Total number of
Observations is the Variance of P
z value correct answers in a normal distribution the value is how many standard deviations the
value lies from the mean, normalizes the numbers in a distribution
units in a normal distribution is
, z= value of random variable -distribution mean/ distribution standard deviation
so for a sample with a expected value of p=.5 and a standard deviation of .05, if you want to
know the proababilty that the estimated fraction lies betweeen .525 and .575 you can find z
values for both of those numbers which tells you the probability that the estimated fraction is to
the right of those numbers and then subtract one from another
Confidence Interval correct answers x̅ +/- t x sd/√n (SE)
if 95% CI for the mean forearm length of men is 24 to 26 cm. this means that we can be 95%
certain that the population mean forearm length for men is within this interval but we CANNOT
say that 95% percent of men have forearms lengths within this interval
CIs do not give any information about the range of individuals
T Test correct answers (x̅ - μ0)/(s/√n) = test statistic
The larger test statistic the smaller the p value because the larger the sample statistic relative to
the standard error
T Distribution correct answers See notes 7-10
Hypothesis Tests correct answers See notes 7-10
Sampling Distribution correct answers With any sample you take you dont have all the
information so you have to take a ton of samples, each one of which gives you a regression line
and a beta (slope), putting all those betas together you get a normal distribution then you take the
mean of all those samples you get the mean of the means which equals the mean of the
population
The variance of the estimates probability distribution reveals the reliability of a an estimate, a
large variance means that it is less likely for the estimate to be close to the actual value
P Value correct answers The probability that the difference between the null and alternative
(sample) test statistic was due to chance
Range of X's Reliability correct answers As the range of x's decreases the reliability decreases
and the variance increases
General Properties of the OLS Estimation Procedure correct answers Treat the coefficient and
constant as random variables so the mean of the estimate's probability distribution equals that of
the population and the variance equals the variance of the error terms probability distribution
divided by the sum of the squared x deviations
When the mean condition above is met the estimation procedure is unbiased and thus does not
over or underestimate the reliability of the estimate
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