Detailed example 1: Restaurants Study
In a study of restaurants, volume of sales (in dollars) is the dependent variable.
One independent variable (x1) is Number of Households in the area (a regular
continuous variable). The other independent variab
Study Aid 2
PIECEWISE LINEAR REGRESSION & DISCONTINUITIES
1. Piecewise Regression - Change of Slope Point Known
Indicator variables can be used to model situations in which the slope of the
regression of Y on X differs for two ranges of X, as in the follo
Study Aid 1
Detailed example 2: Depression Scores Study
The estimated model is (t-ratios in parentheses):
y = 1035.519 -2.859x1 -241.357x2 4.180(x1x2)
(150.01) (-14.06) (-2.07)
The significant interaction effect sug
Lecture Notes 4
1. Formulation of the Model
A regression model with p-1 predictors is called additive if the response
function can be written in the form
Ecfw_y = f1(x1) + f2(x2) + . + fp-1(xp-1)
where f1, f2, ., fp-1 can be any function.
Models that are
Lecture Notes 3
when evaluating the shape of a polynomial response function, it is
necessary to keep within the range of x in the data, as extrapolating
beyond this range may lead to misleading predictions
it is possible to convert from the coeffici
Lecture Notes 2
A nonlinear relationship between y and x can often be approximately
represented within the general linear model as a polynomial function of x.
yi = 0 + 1xi + 2xi2 + i
may be represented as a linear model
yi = 0 + 1xi1 + 2xi2 + i
Lecture Notes 1
Two additional elements of the standard regression output become relevant in
the multiple-regression context.
1. Standardized Regression Coefficients
The standardized regression coefficient bk* is calculated as:
bk* = bk(s(Xk)/s(Y)
Number of Categories
A categorical variable with k classes (categories) is represented by k1 indicators, with one category omitted. Using k indicators to represent a
categorical variable with k classes would make the X'X matrix singular,
so cannot be
Class Assignment 1
1. An indicator (or binary variable) is a variable that can have only two
values, 0 or 1.
Indicator variables are used to
represent qualitative (or nominal or categorical) variables.
2. A qualitative (nominal or categorical) variable wi
Study Aid 3
1. Controlled Experiments
Example: an agricultural experiment to assess the effect on yield of a variety of
corn of three levels of fertilizer and three levels of watering.
Example: Shephard's experiments in which the dependent variable is the