1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome

2. A note on doodling

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

4. Homework on class website:
Please complete homework worksheet #24
Simple Regression Worksheet
Due: Monday, April 17th

5. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Project 4

6. By the end of lecture today 4/12/17
Simple Regression
Using correlation for predictions

7. Project 4 - Two Correlations - We will use these to create 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

9. 3
0.878

11. 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

12. 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.

13. We are measuring 9 students

15. Critical r = 0.666
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SAT (Verbal)
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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) =

16. 4.0
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SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

17. 4.0
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SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

18. 4.0
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SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

19. How to complete scatterplots, correlations and simple regressions using Excel
Real time demo

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. Thank you!
See you next time!!