M349R (56250)
Gustavo Cepparo
Assignment 2
1)
Effect of Outliers and Influential Observations
a. Removing an outlier from negatively associated scatterplot will cause the correlation
to get stronger, meaning that the absolute value of r will get closer to
M349R (56250)
Gustavo Cepparo
Assignment 3
1) Problem 4.4 on Bowerman
a.
b0 = 1523.38924
This is the intercept where the labor hour needed is 1523.38924 when x1=x2=x3=0
(p-value = .0749, therefore we fail to reject H0: 0 = 0)
b1 = .05299
For every increas
HW 2
5. Suppose you have programmed a computer to do the following:
(Simulation R)
i- Draw randomly 100 values from a standard normal distribution.
ii- Multiply each of these values by 5 and add 1.
iii- Average the resulting 100 values.
iv- Call the avera
STA 6253: Time Series Analysis and Applications
Homework #4 (Due Date: Thursday, Oct. 6,2016)
1. Identify the following models as ARMA(p,q) models. Watch out for parameter redundancy. Determine whether they are stationary and/or invertible.
a) Yt = .8Yt1
1. What is heteroskedasticity?
Heteroskedasticity is the violation of the equal (constant) variance
assumption of error terms in regression. A model with heteroskedasticity
usually has inflated (big) t-statistics, caused by small standard errors. This
mig
Review for Test 2 (M349R)
1) From Anova to Regression
2) Use the variance covariance matrix for Testing Linear Hypotheses and
CI construction
3) Write down a model in the context of an experiment or observational
study
3) Heteroskedasticity (All)
4) Colli
Problem 1
Consider a situation where an anthropologist is studying a population of people who
have lived in mountain isolation for several generations. She is interested in studying
the relationship of the height at 18 for males, to the following variable
Problem 4
A study reported by Smith (1967), recorded the level of an enzyme, creatinine kinase
(CK), for patients who were suspected of having a heart attach. The object of the study
was to assess whether measuring the amount of CK on admission to the hos
ods html;
ods graphics on;
/*Two Sample Randomization Test using as a test stat
the sum of the scores of one of the samples*/
data instruction;
input method $ score;
datalines;
new 37
new 49
new 55
new 57
trad 23
trad 31
trad 46
proc npar1way data=instruc
Comparing Two Groups:
Example 1. Morning versus Afternoon.
Afternoon=c(90,87,77,70)
Morning=c(69,71,63)
Sombrero=c(90,87,77,70,69,71,63)
nrep=10000
compare=replicate(nrep,mean(sample(Sombrero,4,replace=F)>=mean(Afternoon)
nyes=sum(compare)
p=sum(compare)/
Quiz 2 M349R Name:_ (5 pts each)
d. The RMSE is 3253.24. Interpret it in the context of the problem.
e. Interpret the coefficient of determination.
f. Use a confidence interval to test for linear hypothesis.
1) Household Expenditure
a. var(et)=2 xt
Table 4a: SAS Output
Variabl
e
Label
Intercep
t
x
Intercep
t
X
Paramet
er
Estimate
DF
1
1
36.75257
0.13391
Standar
d Error
20.0523
2
0.02879
t Value
Pr > |t|
1.83 0.0747
4.65 <.0001
b. var(et)=2 xt
Table 4b: SAS Ou
1) House Price Model
Table 6: SAS Output
Paramet
Variabl
DF
er
e
Estimate
Intercep
t
1
-19.315
sqrft
1
0.12844
bdrms
1 15.19819
Standar
d Error
t Value
31.0466
2
0.01382
9.48352
95% Confidence
Limits
Pr > |t|
-0.62 0.5355
9.29 <.0001
1.6 0.1127
-81.044
0.
1)
College GPA and ACT Scores
a. The value of intercept does not much have meaning in the interpretation of this data,
because the data does not include any point with ACT score = 0. Also, we do not
have enough evidence to say that someone with ACT score
STA 6253: Time Series Analysis and Applications
Chapter 3: Trends in Time Series
Lecture 3 2: Interpreting Regression Output
Least-Squares Estimates of Trend Parameters
Recall that in the regression model
y = X + ,
the least squares estimate of , under th
Hw #3 (STA 6253, Fall 2016)
Due Date: Tuesday, Sept, 27, 2016
Notes:
1. Organize your work neatly.
2. I encourage you to use latex and R knittr to submit a professionally looking homework.
However, I will accept handwritten or processed in any other word
STAT 6253: Time Series Analysis
Chapter 6: Model Specification (Identification)
Lecture 6 1: Tools for Model Identification: Autocorrelation ,
Partial Autocorrelation and Extended Autocorrelation Functions
There are four important steps in model building:
STAT 6253: Time Series Analysis
Chapter 3: Decomposition Methods
Lecture3 3u: Multiplicative and Additive Decomposition
We use decomposition methods to forecast a time series. These models have
no theoretical basis. The time series is decomposed in four p
STA 6253: Time Series Analysis and Applications
Chapter 5: Models for Nonstationary Time Series
Lecture 5 1: Mixed Autoregressive and Moving Average
Processes (ARIMA)
Stationarity Through Differencing
We saw earlier that if there is deterministic trend in
STA 6253: Time Series Analysis and Applications
Chapter 4: Models for Stationary Time Series
Lecture 4 1: General Linear, Autoregressive and Moving Average
Processes
In this chapter we cover a broad class of time series models called Box-Jenkins
ARMA (Aut
STA 6253: Time Series Analysis and Applications
Chapter 3: Trends in Time Series
Lecture 3 1: Trends in Time Series
Estimation of Constant Mean
Consider constant mean model
Yt = + Xt ,
where is a constant mean and E(Xt ) = 0 for all t. Wish to estimate
b
STAT 6253: Time Series Analysis
Lecture 3 4: Modeling Time Series using Regression Analysis
Modelling trend Using Polynomials
Here, we model trend using polynomial functions of time (linear, quadratic).
We assume that the regression coefficients of the tr
STA 6253: Time Series Analysis and Applications
Chapter 4: Models for Stationary Time Series
Lecture 4 2: Mixed Autoregressive and Moving Average
Processes (ARMA)
Now suppose that the model is a mixture of AR and MA components of
orders p and q respective
Chapter 3: Time Series Regression
Lecture 3 5: Exploratory Data Analysis: Dealing With
Nonstationarity
In time series analysis, we need to estimate the dependence structure via autocorrelation between two of its values with precision. This is possible onl
M349R (56250)
Gustavo Cepparo
Assignment 4
1) 1
2) Bowerman 5.15 and 5.16
5.15
a.
Problem 2:
1.
Problem 5.15
Part (a)
All of the residuals except for 3 observations seem to be on the same order of
magnitude
Part(b)
The hospital labor needs, n-(k+2) = 16 (
M349R (56250)
Gustavo Cepparo
Final Assignment
1)
a.
= 78.73426 + 0.53426
Variable
D
F
Intercept
X
1
1
Paramet
Standar
er
d Error
Estimate
78.73426 0.59735
0.53426 0.04098
t Value
Pr > |t|
131.81 <.0001
13.04 <.0001
b.
Durbin-Watson D
Pr < DW
Pr > DW
0.57