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:
No homework due: Monday, April 24th

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

6. By the end of lecture today 4/21/17
Multiple Regression
Using multiple predictor variables (independent) to make predictions about the predicted variable (dependent)
More than one coefficient of regression (also called “b”s or slopes)

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

9. regression coefficient
We refer to the predicted variable as the dependent variable (Y) and the
predictor variable (X) as the independent variable
Why are we finding the regression line? How would we use it?
regression coefficient
(slope)
correlation
coefficient
(“r”)

10. What variable are we predicting?
a. Height of Boys in 1990 (cm) b. Age of boys in 1990
c. Both height and age of boys in 1990

11. Just for fun let’s do the math
If a boy is 8-years old how tall would we predict he would be? Complete prediction “by eye” looking at graph?
a. 40 cm b. 80 cm
c. 120 cm
d. 160 cm
Just for fun let’s do the math
Y’ = (8) = 122

12. Just for fun let’s do the math
If a boy is 2-years old how tall would we predict he would be? Complete prediction “by eye” looking at graph?
a. 40 cm b. 80 cm
c. 120 cm
d. 160 cm
Just for fun let’s do the math
Y’ = (2) = 78.8

13. What variable are we predicting?
a. Size of state (square miles) b. Number of letters in name of state
c. Both size of state and number of letters

14. Just for fun let’s do the math
If a state has 7 letters in the name (like Arizona) how large would we predict the state to be? Complete prediction “by eye” looking at graph?
a. 20,000 square miles b. 30,000 square miles
c. 40,000 square miles
d. 50,000 square miles
Just for fun let’s do the math
Y’ = -2,561.5 (7) + 67,884 = 49,953

15. What variable are we predicting?
a. Size of TV (inches) b. Sales price of TV ($)
c. Both sales price and size of TV

16. Just for fun let’s do the math
If a TV is 55 inches what would we predict cost to? Complete prediction “by eye” looking at graph?
a. $1,500 b. $1,725
c. $2,000
d. $2,225
Just for fun let’s do the math
Y’ = (55) – = $2,235

17. Just for fun let’s do the math
If a TV is 40 inches what would we predict cost to? Complete prediction “by eye” looking at graph?
a. $1,500 b. $1,725
c. $2,000
d. $2,225
Just for fun let’s do the math
Y’ = (40) – = $1,439

18. What variable are we predicting?
a. Amount of Wine Consumed
b. Death Rate in the Country
c. Both Amount of Wine Consumed and Death Rate

19. Just for fun let’s do the math
If a country consumes an average of 8 liters (per capita) what would we predict death rate from heart disease be? Complete prediction “by eye” looking at graph?
a. 50
b. 75
c. 100
d. 125
Just for fun let’s do the math
Y’ = (8) = 75.6

20. 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

21. 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

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

23. 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

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
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.

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
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.

26. 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.

27. 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

28. 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

29. 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?

30. 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”

31. “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

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

33. 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

34. 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’

35. Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
How many dependent variables are in a simple regression and in a multiple regression?
3. How are “slopes”, “b”s, and “regression coefficients” related?
4. Please name each symbol r r2 b
y – y’
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate

36. Simple regression: Predicting sales from number of sales calls made
Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
Simple regression has one predictor variable and one predicted variable
Multiple regression has multiple predictor variables and one predicted variable
How many dependent variables are in a simple regression and in a multiple regression?
3. How are “slopes”, “b”s, and “regression coefficients” related?
4. Please name each symbol r r2 b
y – y’
Examples:
Simple regression: Predicting
sales from number of sales calls
made
Multiple regression: Predicting job
success from age, niceness, and harshness
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate

37. Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
How many dependent variables are in a simple regression and in a multiple regression?
Simple regression has one independent variable and one dependent variable
Multiple regression has multiple independent variables and one dependent variable
3. How are “slopes”, “b”s, and “regression coefficients” related?
4. Please name each symbol r r2 b
y – y’
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate

38. All are names for the same thing
Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
How many dependent variables are in a simple regression and in a multiple regression?
3. How are “slopes”, “b”s, and “regression coefficients” related?
4. Please name each symbol r r2 b
y – y’
All are names for the same thing
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate

39. Coefficient of correlation Coefficient of determination
Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
How many dependent variables are in a simple regression and in a multiple regression?
3. How are “slopes”, “b”s, and “regression coefficients” related?
Coefficient of correlation
4. Please name each symbol r r2 b
y – y’
Coefficient of determination
Coefficient of regression
Residual
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate

40. Can vary from -1 to +1 Can vary from 0 to +1 Any number Any number
Pop Quiz –
How does a multiple regression differ from a simple regression?
(Give an example of each)
How many dependent variables are in a simple regression and in a multiple regression?
3. How are “slopes”, “b”s, and “regression coefficients” related?
4. Please name each symbol r r2 b
y – y’
Can vary from -1 to +1
5. What possible values can each of these have? r r2 b
y – y’
Standard error of the estimate
Can vary from 0 to +1
Any number
Any number
Any positive number

41. Thank you!
See you next time!!