Math 147
Utkarsh J. Dang
Lecture 25
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1/17
Math 147
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The Accuracy of Averages (Chapter 23)
Box models for chance processes:
1. For sum of draws in the context of values of tickets e.g.,
figuring out what a player is likely to
Math 147
Utkarsh J. Dang
Lecture 24
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1/9
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In fall 2005, a city university had 25,000 registered students. To estimate the
percentage who were living at home, a simple random sample of 400 students
was drawn. It turne
Math 147
Utkarsh J. Dang
Lecture 26
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1/17
Math 147
Utkarsh J. Dang
Quick recap
The Central Limit Theorem for sums and averages
When drawing at random with replacement from a box, the
probability histogram for the sum (average) of the draws
Math 147
Utkarsh J. Dang
Lecture 23
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1/16
Math 147
I
Utkarsh J. Dang
Lets use the normal curve to compute chances using the
expected value and SE for a sample percentage.
In a certain town, the telephone company has 100,000 subscribers.
It
Math 147
Utkarsh J. Dang
Lecture 22
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1/15
Math 147
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Using chance in surveys
I
Previously talked about selection bias, non-response bias, and
free choice by investigators using quota sampling.
I
Unintentional bias on the part
Math 147
Utkarsh J. Dang
Lecture 20
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1/17
Math 147
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Recap and looking ahead
The expected value.
I Standard error.
I Normal approximation
I Shortcut for SD.
I Sum of draws vs. counting.
I
Today: The Normal Approximation for
Pr
Project 1: THE 12 MOST PROBABLE EARTH IMPACT ASTEROIDS (JPL Sentry System)
Casey Glaab
MAT 124
23 February 2017
Asteroid
2017:CA33
Year 1
2034
Year 2
2116
1.
Probability
5.6E-09
There are no outliers in the histogram of the velocities.
Velocity(mph)
45521
Math 147
Utkarsh J. Dang
Lecture 15
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1/11
Math 147
Utkarsh J. Dang
Recap and looking ahead
What are the chances?
I Conditional Probabilities
I Multiplication rule.
I
Today: More about Chance (Chapter 14)
2/11
Math 147
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When t
49 itz/Mliohlaw M :z
A
1/ ,)2 Sta, Jwimigrnyhjpw.
cfw_1317 x 59!) : 51> 79w 5 vaqble- , Regression effect
s Regression fallacy
, R.M.S. error for regression
Today: Plotting residuals (Chapter 11) and the
Regression Line (Chapter 12) , Prediction errors ar
Math 147
Utkarsh J. Dang
Lecture 2
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1/21
Math 147
Utkarsh J. Dang
Recap
I
Syllabus, progress outline, and miscellaneous.
I
Introduction to statistics.
I
Example
I
Descriptive statistics.
I
Statistical inference.
I
Experimental design.
2/21
Math 147
Utkarsh J. Dang
Lecture 8
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1/16
Math 147
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Recap and looking ahead
Percentiles.
I Measurement error vs systematic error.
I Chance error vs bias.
I SD of a series of repeated measurements.
I
Today: Descriptive Statisti
Math 147
Utkarsh J. Dang
Lecture 4
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1/16
Math 147
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Recap and looking ahead
I
Observational studies. Why?
I
Are observational studies useful?
I
Controlling for confounding variables
I
Simpsons paradox
Today: Descriptive Statis
Math 147
Utkarsh J. Dang
Lecture 14
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1/17
Math 147
Utkarsh J. Dang
Formally
to the regression line
Slope is the average change in y associated with one
unit increase in x.
I Mathematically,
r SD of y
Slope =
SD of x
I Intercept is the predi
Math 147
Utkarsh J. Dang
Lecture 9
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1/15
Math 147
Utkarsh J. Dang
Recap and looking ahead
Plotting points.
I Equation of a line.
I Bivariate data.
I Positive association.
I Independent and dependent variables.
I
Today: Correlation (covered
Math 147
Utkarsh J. Dang
Lecture 10
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1/14
Math 147
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In-class exam I
First exam will be held in-class on Monday,
September 26th.
I You are responsible for all the material that we have
covered from the beginning of the semeste
Math 147
Utkarsh J. Dang
Lecture 12
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Text
Text
1/16
Math 147
Utkarsh J. Dang
Regression Fallacy
Recall that for the student who scored at the 90th percentile on
the SATs, our regression estimate was the 69th percentile on
the first year exa
Math 147
Utkarsh J. Dang
Lecture 3
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1/22
Math 147
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Recap and looking ahead
I
Controlled experiment. Why?
I
Randomization. Why?
I
Double-blinding. Why?
I
Bias; confounding. Why?
I
Polio vaccine trial.
Today: Observational stud
Math 147
Utkarsh J. Dang
Lecture 6
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1/15
Math 147
Utkarsh J. Dang
Recap and looking ahead
I
Summarizing data using numerical tools.
I
The average, median, root-mean-square, and
standard deviation.
Today: Descriptive Statistics (covered in
C
Math 147
Utkarsh J. Dang
Lecture 5
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1/17
Math 147
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Recap and looking ahead
I
Summarizing data using visual tools.
I
The histogram.
I
Types of variables.
Note about histograms in the text:
I Where are the blocks? Why the smoot
Math 147
Utkarsh J. Dang
Lecture 7
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1/17
Math 147
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Recap and looking ahead
I
Summarizing data using numerical tools.
I
Using the normal approximation for data to figure
out percentages in a given interval.
Today: Descriptive
Math 147
Utkarsh J. Dang
Lecture 11
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1/14
Math 147
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Recap and looking ahead
Correlation.
I r.m.s. vertical distance to the SD line.
I Correlations based on rates or averages: ecological
correlations.
I
Today: Regression (cove