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Lecture 25
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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
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 s
Math 147
Utkarsh J. Dang
Lecture 26
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Math 147
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Quick recap
The Central Limit Theorem for sums and averages
When drawing at random with replacement from a box, the
pr
Math 147
Utkarsh J. Dang
Lecture 23
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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 t
Math 147
Utkarsh J. Dang
Lecture 22
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Math 147
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Using chance in surveys
I
Previously talked about selection bias, non-response bias, and
free choice by investigators
Math 147
Utkarsh J. Dang
Lecture 20
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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
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
Math 147
Utkarsh J. Dang
Lecture 15
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1/11
Math 147
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Recap and looking ahead
What are the chances?
I Conditional Probabilities
I Multiplication rule.
I
Today: More about C
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Lecture 2
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Math 147
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Recap
I
Syllabus, progress outline, and miscellaneous.
I
Introduction to statistics.
I
Example
I
Descriptive statistics
Math 147
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Lecture 8
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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
Math 147
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Lecture 4
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Recap and looking ahead
I
Observational studies. Why?
I
Are observational studies useful?
I
Controlling for confounding
Math 147
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Lecture 14
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Formally
to the regression line
Slope is the average change in y associated with one
unit increase in x.
I Mathematica
Math 147
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Lecture 9
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Recap and looking ahead
Plotting points.
I Equation of a line.
I Bivariate data.
I Positive association.
I Independent
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Lecture 10
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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
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Lecture 12
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Text
Text
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Math 147
Utkarsh J. Dang
Regression Fallacy
Recall that for the student who scored at the 90th percentile on
the SATs, our regression
Math 147
Utkarsh J. Dang
Lecture 3
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Math 147
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Recap and looking ahead
I
Controlled experiment. Why?
I
Randomization. Why?
I
Double-blinding. Why?
I
Bias; confounding
Math 147
Utkarsh J. Dang
Lecture 6
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Recap and looking ahead
I
Summarizing data using numerical tools.
I
The average, median, root-mean-square, and
standard
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Lecture 5
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Recap and looking ahead
I
Summarizing data using visual tools.
I
The histogram.
I
Types of variables.
Note about histog
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Lecture 7
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Recap and looking ahead
I
Summarizing data using numerical tools.
I
Using the normal approximation for data to figure
o
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Lecture 11
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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 avera