1. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2016 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays
Welcome

3. Schedule of readings Study guide for Exam 4 is online
Before our fourth and final exam (May 2nd)
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 #26
Multiple Regressions Worksheet
Due: Wednesday, April 27th

5. By the end of lecture today 4/25/16
Multiple Regression
Using multiple predictor variables (independent) to make predictions about a single predicted variable (dependent) Multiple regression coefficients (b)
One regression coefficient for each independent variable

6. Lab sessions
No more
labs this semester

7. Sample memorandum and general instructions for Project 4 are both online
Due this week in class

8. Review 50% is explained so the other 50% has yet to be explained
(0.71 > 0.632)
Review

9. Summary
Intercept: suggests that we can assume each salesperson will sell at least systems
Slope: as sales calls increase by one, more systems should be sold
Review

10. Some useful terms
Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent)
Coefficient of correlation is name for “r”
Coefficient of determination is name for “r2” (remember it is always positive – no direction info)
Coefficient of regression is name for “b”
Residual is found by y – y’

11. Homework Review

12. For each additional hour worked, weekly pay will increase by $6.09
+0.92
positive
strong
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 up
down
55.286
6.0857
y' = x
207.43
85.71
or 84%
84% of the total variance of “weekly pay” is accounted for by “hours worked”
For each additional hour worked, weekly pay will increase by $6.09

13. 400
380
360
Wait Time
340
320
300
280 4 5 6 7 8
Number of Operators

14. No we do not reject the null
Critical r = 0.878
No we do not reject the null
-.73
negative
strong
The relationship between
wait time and number of operators working is negative and moderate. This correlation is not
significant, r(3) = 0.73; n.s.
number of operators increase, wait time decreases
458
-18.5
y' = -18.5x + 458
365 seconds
328 seconds
or 54%
The proportion of total variance of wait time accounted for by number of
operators is 54%.
For each additional operator added, wait time will decrease by 18.5 seconds

15. 39 36 33 30 27 24 21
Percent of BAs
Median Income

16. Percent of residents with a BA degree
Critical r = 0.632
Yes we reject the null
Percent of residents with a BA degree 10 8
0.8875
positive
strong
The relationship between
median income and percent of residents with BA degree is strong and positive. This correlation is significant, r(8) = 0.89; p < 0.05.
median income goes up so does percent of residents who have a BA degree
3.1819
0.0005
y' = x
25% of residents
35% of residents
or 78%
The proportion of total variance of % of BAs accounted for by
median income is 78%.
For each additional $1 in income, percent of BAs increases by .0005

17. 30 27 24 21 18 15 12
Crime Rate
Median Income

18. No we do not reject the null
Critical r = 0.632
No we do not reject the null
Crime Rate 10 8
negative
moderate
The relationship between
crime rate and median income is negative and moderate. This correlation is not significant,
r(8) = -0.63; p < n.s. [ is not bigger than critical of 0.632] .
median income goes up, crime rate tends to go down
4662.5
y' = x
2,417 thefts
1,418.5 thefts
.396 or 40%
The proportion of total variance of thefts accounted for by
median income is 40%.
For each additional $1 in income, thefts go down by .0499

19. Multiple regression equations
Can use variables to predict
behavior of stock market
probability of accident
amount of pollution in a particular well
quality of a wine for a particular year
which candidates will make best workers

20. Can use variables to predict which candidates will make best workers
Measured current workers – the best workers tend to have highest “success scores”. (Success scores range from 1 – 1,000)
Try to predict which applicants will have the highest success score.
We have found that these variables predict success:
Age (X1)
Niceness (X2)
Harshness (X3)
Both 10 point scales
Niceness (10 = really nice)
Harshness (10 = really harsh)
According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Y’ = b1X 1+ b2X 2+ b3X 3 + a
Y’ = b1 X b X b X a
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

21. According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Y’ = b1 X b X b X a
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

22. According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Y’ = b1 X b X b X a
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
Y’ = b1X 1 + b2X 2 + b3X 3+ a
Y’ is the dependent variable
“Success score” is your dependent variable.
X1 X2 and X3 are the independent variables
“Age”, “Niceness” and “Harshness” are the independent variables.
Each “b” is called a regression coefficient.
Each “b” shows the change in Y for each unit change in its own X (holding the other independent variables constant).
a is the Y-intercept

23. Y’ = b1X 1 + b2X 2 + b3X 3+ a
The Multiple Regression Equation – Interpreting the Regression Coefficients
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
b1 = The regression coefficient for age (X1) is “1”
The coefficient is positive and suggests a positive correlation between age and success.
As the age increases the success score increases. The numeric value of the regression coefficient provides more information.
If age increases by 1 year and hold the other two independent variables constant, we can predict a 1 point increase in the success score.

24. Y’ = b1X 1 + b2X 2 + b3X 3+ a
The Multiple Regression Equation – Interpreting the Regression Coefficients
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
b2 = The regression coefficient for age (X2) is “20”
The coefficient is positive and suggests a positive correlation between niceness and success.
As the niceness increases the success score increases. The numeric value of the regression coefficient provides more information.
If the “niceness score” increases by one, and hold the other two independent variables constant, we can predict a 20 point increase in the success score.

25. Y’ = b1X 1 + b2X 2 + b3X 3+ a
The Multiple Regression Equation – Interpreting the Regression Coefficients
Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
b3 = The regression coefficient for age (X3) is “-75”
The coefficient is negative and suggests a negative correlation between harshness and success.
As the harshness increases the success score decreases. The numeric value of the regression coefficient provides more information.
If the “harshness score” increases by one, and hold the other two independent variables constant, we can predict a 75 point decrease in the success score.

26. Victoria will have a Success Index of 740
Here comes Victoria, her scores are as follows:
Prediction line:
Y’ = b1X 1+ b2X 2+ b3X 3+ a
Y’ = 1X 1+ 20X X
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
Age = 30
Niceness = 8
Harshness = 2
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
What would we predict her “success index” to be?
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
We predict
Victoria will have a Success Index of 740
Y’ =
(1)(30)
+ (20)(8)
- 75(2)
+ 700
= 3.812
Y’ = 740
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

27. What would we predict her “success index” to be?
Here comes Victoria,
her scores are as follows:
Prediction line:
Y’ = b1X 1+ b2X 2+ b3X 3+ a
Y’ = 1X 1+ 20X X
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
Age = 30
Niceness = 8
Harshness = 2
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
What would we predict her “success index” to be?
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
Y’ =
(1)(30)
+ (20)(8)
- 75(2)
+ 700
We predict
Victoria will have a Success Index of 740
Y’ = 740
= 3.812
Here comes Victor,
his scores are as follows:
Age = 35
Niceness = 2
Harshness = 8
We predict
Victor will have a Success Index of 175
What would we predict his “success index” to be?
Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700
Y’ =
(1)(35)
+ (20)(2)
- 75(8)
+ 700
Y’ = 175

28. Can use variables to predict which candidates will make best workers
We predict
Victor will have a Success Index of 175
We predict
Victoria will have a Success Index of 740
Who will we hire?

29. Conducting multiple regression analyses that are relevant and useful starts with measurement designed to decrease uncertainty
“Anything can be measured. If a thing can be observed in any way at all, it lends itself to some type of measurement method. No matter how “fuzzy” the measurement is, it’s still a measurement if it tells you more than you knew before.”
Douglas Hubbard
Author “How to Measure Anything: Finding the value of “Intangibles” in Business”

30. “A problem well stated is a problem half solved”
“Anything can be measured. If a thing can be observed in any way at all, it lends itself to some type of measurement method. No matter how “fuzzy” the measurement is, it’s still a measurement if it tells you more than you knew before.”
Douglas Hubbard
Author “How to Measure Anything: Finding the value of “Intangibles” in Business”
“A problem well stated is a problem half solved”
Charles Kettering (1876 – 1958),
American inventor, holder of 300 patents, including electrical ignition for automobiles
How do we operationally define and measure constructs that we care about?
“It is better to be approximately right, than to be precisely wrong.”
- Warren Buffett
Measurements don’t have to be precise to be useful

31. Thank you!
See you next time!!