1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. Schedule of readings A week from today
Before our fourth and final exam (December 5th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

4. Lab sessions No official Labs this week
TAs available for tutoring help during regular lab times

5. By the end of lecture today 11/28/16
Logic of hypothesis testing with Correlations
Interpreting the Correlations and scatterplots
Simple Regression
Using correlation for predictions

6. Homework - On class website
Please complete homework worksheet #23
Correlations and Simple Regression Worksheet
Due: Wednesday, November 30th
Please complete homework worksheet #24
Review for Exam 4 Worksheet – Handed out in class
Due: Friday, December 2nd

7. Correlation matrices What do we care about?
We measured the following characteristics of 150 homes
recently sold
Price
Square Feet
Number of Bathrooms
Lot Size
Median Income of Buyers

8. Correlation matrices
What do we care about?

9. Correlation matrices
What do we care about?

10. Correlation matrices
What do we care about?

11. α = .05 Critical r value from table df = 148 pairs
Critical value r(148) = 0.195
df = # pairs - 2

12. Only correlation not big enough to reach significance
Correlation matrices
What do we care about?
Only correlation not big enough to reach significance
Critical value from table r(148) = 0.195

13. If price of house and lot size are
What is r2?
r2 = The proportion of the total variance in one variable that is
predictable by its relationship with the other variable
r2 = The proportion of the total variance in [insert dependent variable here] that is
predictable by its relationship with the [insert independent variable here]
Example
If price of house and lot size are
correlated with an r = .50, then what proportion of variance of price is accounted for by lot size?
Price of House
.25 because (.5)2 = .25
We can also say 25% of the variance of price is accounted for by lot size.
Lot Size

14. Correlation matrices What do we care about?
r2 = .53 or 53%
What amount of variance of price is accounted for by square footage?
To find r2 we simply square the r value

15. 3
0.878

17. 3
0.878
Yes
Yes
The relationship between the hours worked
and weekly pay is a strong positive correlation.
This correlation is significant, r(3) = 0.92; p < 0.05

18. 3
-0.73 3
0.878 No No
The relationship between wait time and number of
operators working is negative and strong, but not
reliable enough to reach significance.
This correlation is not significant, r(3) = -0.73; n.s.

19. We are measuring 9 students

21. Critical r = 0.666
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
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1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
Do not reject null
r is not significant
Do not reject null
r is not significant
Reject Null
r is significant
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

22. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

23. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

24. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

25. Correlation: Independent and dependent variables
When used for prediction we refer to the predicted variable
as the dependent variable and the predictor variable as the independent variable
What are we predicting?
What are we predicting?
Dependent
Variable
Dependent
Variable
Independent
Variable
Independent
Variable

26. Correlation - What do we need to define a line
If you probably make this much
Expenses per year
Yearly Income
Y-intercept = “a” (also “b0”) Where the line crosses the Y axis
Slope = “b” (also “b1”) How steep the line is
If you spend this much
The predicted variable goes on the “Y” axis and is called the dependent variable
The predictor variable goes on the “X” axis and is called the independent variable

27. Dustin spends $12 for his Birthday
Angelina Jolie Buys Brad Pitt a $24 million
Heart-Shaped Island for his 50th Birthday
Angelina probably makes this much
Expenses per year
Yearly Income
Dustin probably makes this much
Dustin spent this much
Angelina spent this much
Dustin spends $12
for his Birthday
Revisit this slide

28. Assumptions Underlying Linear Regression
For each value of X, there is a group of Y values
These Y values are normally distributed.
The means of these normal distributions of Y values all lie on the straight line of regression.
The standard deviations of these normal distributions are equal.
Revisit this slide

29. Correlation - the prediction line
- what is it good for?
Prediction line
makes the relationship easier to see
(even if specific observations - dots - are removed)
identifies the center of the cluster of (paired) observations
identifies the central tendency of the relationship (kind of like a mean)
can be used for prediction
should be drawn to provide a “best fit” for the data
should be drawn to provide maximum predictive power for the data
should be drawn to provide minimum predictive error

30. Thank you!
See you next time!!