Regressions Prelim 1

Front 1

Is sample/sample average biased when figuring out the population mean?

Back 1

No, the same average is an unbiased estimator of population mean, if the expected value of the sample average is equal to the population mean. This does not mean the sample average is the population mean, but that in the expected value they are equal. If you take an infinite number of sample averages you will get the population mean.

Front 2

Central limit Theorem

Back 2

the sample size of n increases the distribution of sample average of these random variable approached the normal distribution with a mean and variance (var/n) irrespective of the shape of the underlying distribution of the individual terms Xi. The standard deviation of the distribution of averages is sigma/square root of n.

Front 3

Standard Error

Back 3

when dealing with a sample, the estimate of the standard deviation of the distribution of averages is called the standard error. 〖SE〗_x ̅ =s⁄√n

Front 4

Expected Value

Back 4

what we expect is going to happen on average in the future if we repeat the experiment a large number of times

Front 5

mode

Back 5

useful for qualitative purposes to determine which variable is "most"

Front 6

median

Back 6

is more useful than mean when there are outliers, median is not as responsive to outliers

Front 7

standard deviation

Back 7

variance of random variable "x", the average distance of each observation from the mean

Front 8

population standard deviation

Back 8

to estimate it you have to find the sample standard deviation

Front 9

The Central Limit Theorem indicates that the distribution of sample averages will be normal, why is this useful?

Back 9

we know a lot about the normal distribution, lots of things in nature look like a normal distribution.

Front 10

The standard normal distribution

Back 10

the standard normal variable Z is a normal random variable with a mean of 0 and a standard deviation of 1

Front 11

Confidence Interval

Back 11

how close is the average to the mean?

Front 12

T-values

Back 12

if we don't know the population standard deviation, we can use an estimate (sample standard deviation), now that there is uncertainty it is not valid to use z-values, have to use t-values

Front 13

z-value vs. t-value

Back 13

z-value works for every sample size, whereas there is one t-value per sample size

Front 14

when to use n-1, and when to use n-2 for degrees of freedom

Back 14

n-1: degree of freedom for population mean

n-2: degree of freedom for slope/regression

Front 15

the 95% confidence interval for the population mean is 160-180, what does that mean?

Back 15

the sample average is estimated to be 170. We never know the exact population mean, we only have an unbiased estimate of it.

Front 16

importance of confidence interval range

Back 16

better to have a narrow range, that way we are more sure of the estimated sample average

Front 17

how to get a narrower confidence interval?

Back 17

increase the sample size, make "n" bigger to make the rest of the equation smaller (it is the only variable we can control)

Front 18

if you wanted to increase the probability that them mean is within a specific range, what could you do?

Back 18

go to a higher confidence interval (1-a)% = a bigger number

Front 19

sample size and bias

Back 19

the sample size has no effect on whether the sample is biased or not, bias is not a function of sample size

Front 20

Standard Normal Distribution

Back 20

mean =0, standard deviation =1

0+/-1 st.dev = 68%

0+/-2 st.dev = 95.4%

0+/-3 st.dev = 99.6%

Front 21

4 components of the central limit theorem

Back 21

1- sample average

2-sample standard deviation

3-standard error

4- distribution of averages

Front 22

Errors are not homoskedastic, does that mean the slope and intercept are biased?

Back 22

homoscedastic errors do not affect bias, as long as the four assumptions hold true the slope and intercept are not biased, regardless of the distribution of errors