1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome
4/20/18

2. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
Row A 15 14
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Harvill 150
renumbered
table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk

4. Schedule of readings Before our fourth and final exam (April 30th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions
Study guide now online

5. Lab sessions
Project 4
Continues

8. 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’
Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation)

9. 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
Review

10. 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
Review

11. 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

12. 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

13. 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?

14. 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”

15. “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

16. Pop Quiz –

17. Simple regression: Predicting sales from number of sales calls made
Pop Quiz –
Simple regression has one predictor variable and one predicted variable
Multiple regression has multiple predictor variables and one predicted variable
Examples:
Simple regression: Predicting
sales from number of sales
calls made
Multiple regression: Predicting
job success from age, niceness,
and harshness

18. Pop Quiz –
Simple regression has one independent variable and one dependent variable
Multiple regression has multiple independent variables and one dependent variable

19. All are names for the same thing
Pop Quiz –
All are names for the same thing

20. Coefficient of correlation Coefficient of determination
Pop Quiz –
Coefficient of correlation
Coefficient of determination
Coefficient of regression
Residual

21. Pop Quiz –
Can vary from -1 to +1
Can vary from 0 to +1
Any number
Any number
Any positive number

22. Multiple Linear Regression - Example
Can we predict heating cost?
Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature, (2) the number of inches of insulation in the attic, and (3) the age in years of the furnace.
To investigate, Salisbury's research department selected a random sample of 20 recently sold homes. It determined the cost to heat each home last January

28. Multiple Linear Regression - Example

29. The Multiple Regression Equation – Interpreting the Regression Coefficients
b1 = The regression coefficient for mean outside temperature
(X1) is
The coefficient is negative and shows a negative correlation between heating cost and temperature.
As the outside temperature increases, the cost to heat the home decreases. The numeric value of the regression coefficient provides more information. If we increase temperature by 1 degree and hold the other two independent variables constant, we can estimate a decrease of $4.583 in monthly heating cost.

30. The Multiple Regression Equation – Interpreting the Regression Coefficients
b2 = The regression coefficient for mean attic insulation (X2) is
The coefficient is negative and shows a negative correlation between heating cost and insulation.
The more insulation in the attic, the less the cost to heat the home.
So the negative sign for this coefficient is logical. For each additional inch of insulation, we expect the cost to heat the home to decline $14.83 per month, regardless of the outside temperature or the age of the furnace.

31. The Multiple Regression Equation – Interpreting the Regression Coefficients
b3 = The regression coefficient for mean attic insulation (X3) is 6.101
The coefficient is positive and shows a negative correlation between heating cost and insulation.
As the age of the furnace goes up, the cost to heat the home increases.
Specifically, for each additional year older the furnace is, we expect the cost to increase $6.10 per month.

33. Applying the Model for Estimation
What is the estimated heating cost for a home if:
the mean outside temperature is 30 degrees,
there are 5 inches of insulation in the attic, and
the furnace is 10 years old?

34. Thank you!
See you next time!!