Math 147
Utkarsh J. Dang
Lecture 15
Utkarsh J. Dang
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
Utkarsh J. Dang
When t
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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
Utkarsh J. Dang
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 7
Utkarsh J. Dang
1/17
Math 147
Utkarsh J. Dang
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 5
Utkarsh J. Dang
1/17
Math 147
Utkarsh J. Dang
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 6
Utkarsh J. Dang
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 3
Utkarsh J. Dang
1/22
Math 147
Utkarsh J. Dang
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 12
Utkarsh J. Dang
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 10
Utkarsh J. Dang
1/14
Math 147
Utkarsh J. Dang
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 9
Utkarsh J. Dang
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 14
Utkarsh J. Dang
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 4
Utkarsh J. Dang
1/16
Math 147
Utkarsh J. Dang
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 8
Utkarsh J. Dang
1/16
Math 147
Utkarsh J. Dang
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 11
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1/14
Math 147
Utkarsh J. Dang
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