CASE STUDIES
DEP2004
METHODS IN DEVELOPMENT
PROFESSOR JONES
BY: KYLE VASQUEZ
WHAT IS A CASE STUDY?
When
a case study is conducted it means that the person
studying is conducting a very in-depth investigation on a
single person, group, or event. While con
Age
in
years
2-4
5-8
9-12
Physical Development
Cognitive
Development
Socioemotional
Development
In ages 2-4 children
learn to:
Stand up
Walk/run
Climb stairs
Jump
In ages 2-4 children learn
to:
Store memories
Imitate language
In ages 5-8 children
le
Kyle Vasquez
AP English literature
1/3/17
Period 4
Foible Essay
I run, I fear the mundane and so, I constantly move from one activity onto the next one.
One day during my freshman year I speed out of my Key Club meeting and ran to my
Choir Conservatory re
Before revision
After revision
Seeing the word cloud made me realize that my essay had a lot more mistakes than I had
thought, I also realized the importance of revising your essay more than once. When I
intentionally wrote the essay I revised it over thr
Additional Theoretical Considerations
Testing Correlation - I
Recall the tests on 1 below all test whether the explanatory &
response variable are related:
Non-equality H0: 1 = 0 vs. Ha: 1 0 - Tests whether there is any
relationship between the response
The Fixed Intercept Model
Introduction
Sometimes, the nature of a problem dictates that when the
explanatory variable is equal to 0, the conditional mean of the
response variable (or response variable itself) be equal to a fixed, a
priori value.
These k
Distributional Properties of the SLM
Inference for 0
Though, the distribution of the LSE for the intercept is normal, the
value of 2 is unknown. Consequently for inference on must use
~ Norm 0,1
0 0
t
0 0
2
n
nSS xx
2
x
i
i 1
s .e. 0
2
nSS xx
2
n
2
x
Distributional Properties of the LSEs
Maximum Likelihood: Motivating
Example - I
Suppose we flip a coin n times. Let p be the probability any given
coin flip turning up heads.
Let 1 denote the outcome is a heads and 0 denote the outcome is a
tails. The
Robust Regression
The Objective Function
Recall the form of the objective function that is minimized to find the
least squares estimates
n
n
S 0 , 1 yi 0 1 xi ei2
i 1
2
i 1
The least squares estimates are the coefficient values that will minimize
the su
Outliers
Outlier Detection
As mentioned earlier an outlier is any observation/s that look
unusual. These can be spotted a priori by constructing a scatter plot
of the response variable versus the explanatory variable.
Whether the presence of outliers is
Mathematical & Stastical Properties
of the LSEs
Identities Involving the LSEs - I
1) The least squares line goes through the centroid of the data (i.e.
the point x , y ).
0 1 x y 1 x 1 x y
2) The sum of the residuals is equal to 0.
n
n
e y
i
i 1
n
i
i
Addressing Model Deviations Methods
Addressing Model Deviations
As mentioned in the last lecture, one must check that the assumptions
made regarding the linear model are satisfied both before fitting the
SLM model and afterwards.
If any of the prior dis
Addressing Model Deviations: Invariance
& Equivariance Considerations
Example 1 - I
For the data on the left, the
relationship between the
response & explanatory
variable appears to follow a
power relationship.
Lets try the transformation
u = x3.
Exampl
Addressing Model Deviations:
Theoretical Considerations
Injective Functions - I
Note that all the functions suggested for transforming variables are
strictly monotonic functions (or compositions of monotone functions)
on the domain of interest thus they
The Simple Linear Model
Simple Linear (Regression) Model
(SLM)
Given bivariate data (X, Y), the population regression model is:
Explanatory/Independent/Regressor/Exogenous
/Predictor/Input Variable or Covariates
Slope (sometimes just called )
Y x 0 1 x |