Download Regression

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Regression analysis wikipedia, lookup

Linear regression wikipedia, lookup

Data assimilation wikipedia, lookup

Regression toward the mean wikipedia, lookup

Choice modelling wikipedia, lookup

Coefficient of determination wikipedia, lookup

Instrumental variables estimation wikipedia, lookup

Forecasting wikipedia, lookup

Interaction (statistics) wikipedia, lookup

Transcript
ANOVA continued and Intro to
Regression
I231B QUANTITATIVE METHODS
Agenda
2
 Exploration and Inference revisited
 More ANOVA (anova_2factor.do)
 Basics of Regression (regress.do)
It is "well known" to be "logically
unsound and practically misleading" to
make inference as if a model is known
to be true when it has, in fact, been
selected from the same data to be used
for estimation purposes.
- Chris Chatfield in "Model Uncertainty, Data Mining and Statistical
Inference", Journal of the Royal Statistical Society, Series A, 158 (1995),
419-486 (p 421)
3
Never mix exploratory analysis with inferential
modeling of the same variables in the same dataset.
4

Exploratory model building is when you hand-pick some
variables of interest and keep adding/removing them
until you find something that ‘works’.

Inferential models are specified in advance: there is an
assumed model and you are testing whether it actually
works with the current data.
Basic Linear Regression
5
(ONE IV AND ONE DV)
Regression versus Correlation
6
 Correlation makes no assumption about one whether one
variable is dependent on the other– only a measure of
general association
 Regression attempts to describe a dependent nature of one
or more explanatory variables on a single dependent
variable. Assumes one-way causal link between X and Y.
 Thus, correlation is a measure of the strength of a
relationship -1 to 1, while regression measures the exact
nature of that relationship (e.g., the specific slope which is
the change in Y given a change in X)
Basic Linear Model
7
 Yi = b0 + b1xi + ei.

X (and X-axis) is our independent variable(s)

Y (and Y-axis) is our dependent variable

b0 is a constant (y-intercept)

b1 is the slope (change in Y given a one-unit
change in X)

e is the error term (residuals)
Basic Linear Function
8
Slope
9
But...what happens if B is negative?
Statistical Inference Using Least Squares
10
 We obtain a sample statistic, b,
which estimates the population
parameter.
 We also have the standard error
for b
 Uses standard t-distribution
with n-2 degrees of freedom for
hypothesis testing.
Yi = b0 + b1xi + ei.
Why Least Squares?
11
 For any Y and X, there is one and only one line of
best fit. The least squares regression equation
minimizes the possible error between our observed
values of Y and our predicted values of Y (often
called y-hat).
Data points and Regression
12
 http://www.math.csusb.edu/faculty/stanton/m262/
regress/regress.html