Tutorial 5 1. Suppose we have n = 10 observations (Xi , Yi ) and t the data with model Yi = 0 + 1 Xi + i with i , i = 1, ., 10 are IID N (0, 2 ). We have the following calculations.
n
X = 0.5669,
n i
TUTORIAL 3 1. Refer to the Grade point average problem (see tutorial 1) (a) obtain a 95% percent interval estimate of the mean freshman GPA for students whose ACT test score is 28. Interpret your cond
Solution to TUTORIAL 3 1. (R code) (a) [3.061384, 3.341033] on average, with 95% condence, the mean freshman GPA is between 3.061384 and 3.341033 when their ACT test scores are 28 (b) [1.959355, 4.443
Tutorial 7 1. A student stated: Adding predictor variables to a regression model can never reduce R2 , so we should include all available predictor variables in the model. Comment. 2. For a model with
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Chapter 10
Comparing Two Groups
Bivariate Analyses: A Response Variable
and a Binary Explanatory Variable
Methods for comparing two groups are special cases of
bivariate statistical methods.
The outc
Chapter 3
Association: Contingency,
Correlation, and Regression
Section 3.1
The Association Between
Two Categorical Variables
Response and Explanatory Variables
Response variable (Dependent Variable)
Chapter 5
Probability
5.1 How Probability Quantifies Randomness
5.2 Finding Probabilities
5.3 Conditional Probabilities
5.4 Applying the Probability Rules
Random Phenomena
For random phenomena, the ou
Recitation Week 12
Problems: 9-10; 9-19; 9-26; 9-28; 9-43; 9-58.
9-10. A wall clock on Planet X has two hands that are aligned at midnight and turn in the
same direction at uniform rates, one at 0.043
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2016/17 Semester 2
1.
ST3131 Regression Analysis
Tutorial 8
The table below gives the systolic blood pressure (y), bod
ST3131 (2016/2017 Semester 2) Partial Solutions/Hints to Questions in Tutorial 3
Note: The solutions provided in this document are for reference only.
Question 1
(i) The model is given by
= 0 + 1 ()
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2016/17 Semester 1
1.
ST3131 Regression Analysis
Tutorial 3
The table below provides data on infant mortality (infant
ST3131 (2016/2017 Semester 2) Partial Solutions/Hints to Questions in Tutorial 1
Note: The solutions provided in this document are for reference only.
Question 1
(i) Model: = + , where
= (2.1 2.3 3.1
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2016/17 Semester 2
1.
ST3131 Regression Analysis
A regression model
data were summarized as follows.
33
289
85
Tutoria
Chapter 6
Probability Distributions
Section 6.1
Summarizing Possible Outcomes and Their
Probabilities
1
Randomness
A random variable is a numerical measurement of the
outcome of a random phenomenon.
O
Chapter 10
Additional nodes:
Logic behind inferential methods
for comparing two groups
(Independent Samples)
Comparing Two Proportions
Comparing Two Proportions:
Confidence Interval Methods
If the fol
Solutions to Tutorial 2 1. (a) Y = 10.2 + 4.00X (SE ) (0.6633) (0.4690) M SE = 2.199289, see code (R code) for the plot. Yes, the linear regression function ts the data well. (b) Y = 10.2 + 4.00 1 = 1
Solutions to Tutorial 4 1. An output of a simple linear regression model Yi = 0 + 1 Xi + i , is as follows Coecients: Estimate Std. Error t value P-value (Intercept) -0.07727 0.12005 -0.644 0.537814 x
Tutorial 5 1. Suppose we have n = 10 observations (Xi , Yi ) and t the data with model
Yi = 0 + 1 Xi + i with i , i = 1, ., 10 are IID N (0, 2 ). We have the following calculations.
n
X = 0.5669,
n i
Solution to Tutorial 6 1.
For each of the following regression models, indicate whether it is a general linear regression model. If not, state whether it can be expressed in the form of a linear regre
Tutorial 7 1.
A student stated: Adding predictor variables to a regression model can never reduce R2 , so we should include all available predictor variables in the model. Comment.
Bigger R2 , means t
Tutorial 10 1. Derive the weighted least square normal equations for tting a simple linear regression func2 tion when i = kXi , where k > 0 is a constant.
Let Qw (b0 , b1 ) =
n i=1
1 (Yi b0 b1 Xi )2 k
Tutorial Questions 1 1. For model Yi = 0 + 1 Xi + i assume that X = 0 is within the scope of the model. What is the implication for the regression function Yi = 0 + 1 Xi if 0 = 0 so that the model is
Tutorial 2 1. Airfreight breakage A substance used in biological and medical research is shipped by airfreight to users in cartons of 1000 ampules. In the (data), X is the number of times the carton w