Lecture 6 - Inference for Single Samples
You know already for a large sample, you can invoke the CLT so:
X N (, 2 ).
Also for a large sample, you can replace an unknown by s.
You know how to do a hypothesis test for the mean, either:
calculate z-statis
Probability Review
A probability space, dened by Kolmogorov (1903-1987) consists of:
A set of outcomes S, e.g.,
for the roll of a die, S = cfw_1, 2, 3, 4, 5, 6,
1 , 1 , 2 , 1 ,., 6
for the roll of two dice, S =
1
2
1
3
6
temperature on Monday, S = [50, 5
Lecture 5 - Basic Concepts of Inference
Statistical Inference is the process of making conclusions using data that is subject
to random variation.
Here are some basic denitions.
Bias() := E() , where is the true parameter value and is an estimate of
it c
Lecture 4 - Condence Intervals
Instead of reporting a point estimator, that is, a single value, we want to
report a condence interval [L, U ] where:
P cfw_L U = 1 ,
the probability of the true value being within [L, U ] is pretty large.
Here, [L, U ] is
Lecture 10 : Multiple Linear Regression
We have:
height weight
.
person 1:
x11
x12
. . . person 2:
x21
age
x1k
x2k
amount of
lemonade
purchased
y1
y2
x22
.
:
where we assume
Yi = 0 + 1 xi1 + 2 xi2 + + k xik + t i
for i = 1, . . . , n and t i N (0, 2 ). Th
Lecture 9 Notes, Regression and Correlation
Regression analysis allows us to estimate the relationship of a response
variable to a set of predictor variables
Let
x1 , x2 , x
n
be settings of x chosen by the investigator and
be the corresponding values of
Lecture 2 - Summarizing Numerical Data
Here are some ways we can summarize data numerically.
Sample Mean:
i=1
xi
n
x :
=
Note: in this class we will work with both the population mean and the sample
mean x. Do not confuse them! Remember, x is the mean of
Lecture 8- Inference for Proportion and Count Data
We want to estimate the proportion p of a population that have a specic attribute,
like what percent of houses in Cambridge have a mouse in the house?
We are given X1 , . . . , Xp where Xi s are Bernoulli