STAT 242: Intermediate Stats
Practice Exam 1: Solutions
1. (a) The command model1=lm(Miles~Min) fits the model and gives
(i)
.
(ii) The t-statistic is 12.78 and the P-value is 1.05e-15 essentially zero. There is very strong
evidence that Min is related to
STAT 242: Intermediate Stats
Exam 1 Practice Exam (includes data analysis component NOT ON ACTUAL EXAM!)
Unlessotherwisespecified,assumea5ignificancelevelforanytestsand95%confidence
levelforanyintervals.
SomeofthequestionsonthisexamwillrefertothedatasetWa
76
Chapter 5
Chapter 5 Solutions
5.1 True. The two-sample pooled t-test is the version of the t-test that assumes that the variances
in the two groups are the same.
5.3 False. The samples must be representative of the population in order to generalize the
88
Chapter 6
Chapter 6 Solutions
6.1
a. The researchers measured the calcium concentration in the plasma of each bird after the
birds were treated so this is the response variable.
b. The two factors were sex and additive given to the birds.
c. Sex was ob
STAT 242: April 5, 2017
Today:
Two-Way ANOVA wrap up
Two-Way ANOVA lab
HW 6 due FRIDAY!
Proposal revisions also due FRIDAY
Two-way ANOVA: Main Effects Model
Y k j
Grand
Mean
Effect for kth
treatment
Effect for jth
block
Random
error
Factorial AnovaE
STAT 242: March 29, 2017
Today:
One-Way ANOVA
Two-Way ANOVA
Friday:
Wrap up Two-Way ANOVA
ANOVA lab
ANOVA for Difference in K Means
Data: Samples from K different groups
Summary statistics: n1 Y1
s1
n2 Y2
s2
nK
YK
n Y
SY
Combine all
sK
Test: H0: 1 =
STAT 242: Spring 2017
Homework #2: SOLUTION
Due Wednesday, February 8 at the beginning of class
From your textbook, do the following problems:
Chapter 1: 1.8, 1.16, 1.23, 1.24
You can find the data under Datasets on moodle.
STAT 242: Spring 2017
Homework #1: SOLUTION
Due Wednesday, February 1 at the beginning of class
From your textbook, do the following problems:
Chapter 0: 0.2, 0.6
Chapter 1: 1.2, 1.3, 1.4, 1.6
STAT 242: March 6, 2017
Today:
Predictor Selection methods
Wednesday: Lab!
Friday: No class ONLINE quiz on moodle
Example: Predicting FY GPA
Data: FirstYearGPA
from Chapter 4
Response: GPA
Predictors: HSGPA
Male
FirstGen
SATV
HU
White
SATM
SS
CollegeB
STAT2 Final Exam Version 1 solutions
1. (a) H0: l= m= h
HA: H0 is false
summary(aov(ROT~BACT) gives us the following: F = 8.087; P-value =0.00089 so
reject H0. We conclude that there is a difference in population mean rot levels among the
bacteria groups.
Statistics 242: February 6, 2017
Today:
Influential points handout
Inference for the slope
ANOVA for the model?
Next time:
More inference for the regression
HW 2 due
Sampling Distribution
Recall:
CLT The sample mean, Y, varies from
sample to sample
Stat 242: February 1, 2017
Today:
Transformations of variables
Outliers, influential points, leverage points
HW 1 due
Friday:
Lab on SLR
What to Do When Regression
Conditions Are Violated?
Examples:
1. Lack of normality in residuals
2. Patterns in r
Statistics 242: January 30, 2017
Today:
A review of Single Linear Regression (SLR)
Next class:
More with SLR and inference
REMEMBER! HW1 due Wednesday(?)
Single Quantitative Predictor Model
Notation:
Y = Response variable
X = Predictor variable
Assum
Statistics 242: February 22, 2017
Today:
Testing subsets of predictors
Polynomial regressions
Looking ahead
HW 4
Exam in ONE week (Chapters 0-3)
Dont need anything except simple calculator and
something to write with.
Interaction
Recall:
Active o 1
Statistics 242: February 20, 2017
Today:
CIs/PIs for MLR
Comparing regression lines
Next time:
Polynomial regressions and correlated predictors (some of 3.4,
3.5)
REMINDER:
HW 4 due next week, but you could start it now!
Recall: Multiple Regression
Statistics 242: February 15, 2017
Today:
Introduction to multiple regression
Quiz 1 return
Next time:
Short lab
More multiple regression info
Simple Linear Regression Model
Y = 0 + 1 X +
where ~ N(0, ) and independent
Multiple Regression Model
Y =
Statistics 242: February 8, 2017
Today:
More ways to assess the fit of a model
Prediction intervals
HW 2 due!
Next time:
Short quiz
Part 2 of SLR lab
ANOVA for Regression
Data
TOTAL
variation in
response, Y
=
Model
=
Variation
explained by
MODEL
+
We have a Fourier representation for the triangle function
x
0 x < 1/2
1 x 1/2 < x 1
f (x) =
(1)
namely
f (x)
=
bm sin(mx)
(2)
m=1
bm
4
=
m2 2
sin
m
2
.
(3)
The Fourier series makes sense even outside the domain of the original function
f . For values of
Math 339, homework problem due Monday Oct. 26, 2009.
1. Let the integral operator K act on functions g in L2 [0, 1] that vanish at the
endpoints x = 0 and x = 1 by
1
(Kg )(x) =
K (x, x )g (x )dx
(1)
0
where the kernel function K (x, x ) is the one from th
Math 339, homework problem due Wednesday Oct. 21, 2009.
1. Let the integral operator K act on functions g in L2 [0, 1] that vanish at the
endpoints x = 0 and x = 1 by
1
(Kg )(x) =
K (x, x )g (x )dx
(1)
0
where the kernel function K (x, x ) is the one from
Math 339, homework problem due Monday Oct. 19, 2009.
1. Consider the 2-point boundary value problem on the interval [0,1]
d2 f
dx2
f (0) = f (1)
= g (x)
(1)
=
(2)
0.
Verify by direct computation that the solution is
1
f (x) =
K (x, x )g (x )dx
(3)
K (x, x