1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
April 10

2. The
Green
Sheets

3. Schedule of readings Before our fourth and final exam (April 29th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

4. Labs continue this week
Lab sessions
Labs continue this week

5. Project 4 - Two Correlations - Two Regression Analyses
This lab builds on the work we did in our very first lab. But now we are using the correlation for prediction. This is called regression analysis
Project 4 - Two Correlations - Two Regression Analyses

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. Correlation matrices What do we care about?
Critical value from table r(148) = 0.195

13. 3
0.878

15. 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

16. 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.

17. We are measuring 9 students, (n=9)
Degrees of freedom
(n-2)
9 – 2 = 7
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) =

18. 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) =

20. Critical r = 0.666
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)
Do not reject null
r is not significant
Reject Null
r is significant
Do not reject null
r is not significant
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

21. 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

22. 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

23. Dustin spends $12 for his Birthday
Jay Z Buys Beyonce a $20 million
Heart-Shaped Island for her 29th Birthday
Jay Z probably makes this much
Expenses per year
Yearly Income
Dustin probably makes this much
Dustin spent this much
Jay Z spent this much
Dustin spends $12
for his Birthday
Revisit this slide

24. 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

25. 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

26. Predicting Restaurant Bill
Prediction line
Y’ = a + b1X1
Cost will be about 95.06
Predicting Restaurant Bill
Cost
Y-intercept
The expected cost for dinner for two couples (4 people) would be $ Cost = Persons
People
If People = 4
Slope
If “Persons” = 4, what is the prediction for “Cost”?
Cost = Persons
Cost = (4)
Cost = = 95.06
If “Persons” = 1, what is the prediction for “Cost”?
Cost = Persons
Cost = (1)
Cost = = 35.18

27. Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (800) Rent = 150 + 840 = 990
Prediction line
Y’ = a + b1X1
Rent will be about 990
Predicting Rent
Cost
Y-intercept
Slope
If SqFt = 800
Square Feet
The expected cost for rent on an 800 square foot apartment is $ Rent = SqFt
If “SqFt” = 800, what is the prediction for “Rent”?
Rent = SqFt
Rent = (800)
Rent = = 990
If “SqFt” = 2500, what is the prediction for “Rent”?
Rent = SqFt
Rent = (2500)
Rent = = 2,775

28. Thank you!
See you next time!!