STA2020F 2007
Class Test 1
Date: 28th March 2007
Total marks: 60
Time: 1 hour 30 minutes
Instructions: Answer all the questions in your blue answer book. Your answer
should be T or F for each question
F distribution
f-test
Tim Low
February 18, 2015
1 / 16
F distribution
A very important set of hypothesis tests in statistics is the two
sample t-test but this test cannot be conducted until we know
wh
February 23, 2015
ANOVA and t-tests of 2 means
Completely Randomised Design
Why do we need the analysis of variance? Why not test every pair of
means? For example say k = 6. There are C26 = 6(5)/2= 14
February 25, 2015
Checking the Required Conditions
Violation of the Required Conditions
The F-test of the analysis of variance requires that the
random variable be normally distributed with equal
vari
March 4, 2015
Two-Factor Analysis of Variance
Two-Factor Analysis of Variance
At the start of this course we addressed problems where the
data were generated from single-factor experiments.
In factori
February 19, 2015
Example 1
IDENTIFY
The null hypothesis in this case is:
H0: 1 = 2 = 3
Test Statistic
Since 1 = 2 = 3 is of interest to us, a statistic that
measures the proximity of the sample means
March 4, 2015
Example 17
Example 17
A two factor analysis of variance experiment was performed
with a = 3, b = 4 and r = 20. The following sums of squares
were computed:
SS(Total) = 42450
SS(A) = 1560
February 26, 2015
Example 10
Example 10
A pharmaceutical company has recently developed four new
drugs to lower cholesterol levels.
To determine whether any differences exist in their benets,
an exper
February 25, 2015
Analysis of Variance Experimental Designs
Independent Samples and Blocks
Experimental design determines which analysis of variance
technique we use.
Similar to the matched pairs expe
March 4, 2015
Example 12
Example 13
The accompanying table presents data on yields relating to resistance to stain for
three materials (M1, M2 and M3) treated with four chemicals in a randomized block
February 18, 2015
Analysis of Variance
Analysis of variance is a technique that allows us to
compare two or more populations of interval data.
Analysis of Variance
Analysis of variance is:
an extreme
t-test
Assumptions
Tim Low
February 16, 2015
1 / 10
The two-sample t-test
In real problems it is virtually always the case that the values of
the population variances are unknown. If the sample sizes
Time series
Forecasting
Tim Low
April 20, 2015
1/1
Forecasting
In forecasting we use data from the past in predicting the future
value of the variable of interest, such as appliance sales, natural
gas
March 11, 2015
Coefficient of Determination
Coefficient of Determination
Tests thus far have shown if a linear relationship exists; it is
also useful to measure the strength of the relationship. This
March 9, 2015
Regression Analysis
Our problem objective is to analyze the relationship
between interval variables; regression analysis is the rst
tool we will study.
Simple Linear Regression
and Corre
March 11, 2015
Multiple Regression
The simple linear regression model was used to analyze how
one interval variable (the dependent variable y) is related to
one other interval variable (the independen
Hypothesis (Goodness of Fit) Test
for Proportions of a Multinomial Population
Tests of Goodness of Fit
Goodness of Fit Test: A Multinomial Population
n Goodness of Fit Test: Poisson
and Normal Distri
Determining When to Add or Delete Variables
Regression Analysis: Model Building
Variable Selection Procedures
Multiple Regression Approach to Experimental Design
The F Test is based on a determination
Time series
Seasonal Indexes
Tim Low
April 16, 2015
1/1
Seasonal Indexes
Depending on the nature of the time series, strong seasonal
patterns may be present for certain months or quarters.
Depending o
Time series
Smoothing techniques
Tim Low
April 14, 2015
1/1
Components of a Time Series
2/1
Moving averages
The moving average replaces the original time series with
another series, each point of whic
Multiple Regression Diagnostics
Tim Low
April 8, 2015
Introduction
Assumptions
Normality
Expectation of 0
Homoscedasticity
Independence
Plots
Residuals vs. predicted values
Residuals vs. explanatory v
April 16, 2015
Regression Analysis
Model Building
Regression analysis is one of the most powerful and
commonly used techniques in statistics; it allows us to create
mathematical models that realistica
Variable Selection: Best-Subsets Regression
Variable Selection: Best-Subsets Regression
The three preceding procedures are one-variable-at-atime methods offering no guarantee that the best
model for a
April 16, 2015
Time Series Models
Time Series Models
There are many models that are available for forecasting a time
series.
Alternatively, we assume that the relationship is multiplicative
In order
April 16, 2015
Time Series Analysis
A variable measured over time (in sequential order) is called
a time series. From this data, we analyze it to detect patterns
that will enable us to forecast future
March 18, 2015
Qualitative Independent variables
Example 3
In many situations we must work with qualitative independent
variables such as gender (male, female), method of payment (cash,
cheque, credit
Example 2
Example 2, cont.
An efficiency expert has studied 12 employees
who perform similar assembly tasks, recording
productivity (units per hour), number of years of
experience, and which one of t
March 11, 2015
Regression Diagnostics
Residual Analysis
There are three conditions that are required in order to
perform a regression analysis. These are:
The error variable must be normally distribu
STA2020F 2009
Class Test 1
Date: 27th March 2009
Total marks: 70
Time: 1 hour 30 minutes
Instructions: Answer all the questions in your blue answer book. Your
answer should be T or F for each question