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Cabinet

Cabinet

Lecturer’s desk

Table

Computer Storage Cabinet

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INTEGRATED LEARNING CENTER

ILC 120

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broken

desk

Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Spring, 2014Room 120 Integrated Learning Center (ILC)10:00 - 10:50 Mondays, Wednesdays & Fridays.

Welcome

http://www.youtube.com/watch?v=oSQJP40PcGI

Before next exam (Monday May 5th)

Please read chapters 10 – 14

Please read Chapters 17, and 18 in Plous

Chapter 17: Social Influences

Chapter 18: Group Judgments and Decisions

Homework due – Friday (April 25th)

- On class website:
- Please complete homework worksheet #21
- Assignment 21: Write 3 multiple choice questions based on any lecture since last exam (April 11th). Bring two copies to class. Each multiple choice question must contain:
- a person’s name
- only one correct answer, and 3 incorrect options (for a total of 4 options for each question)
- Due: Friday, April 25th

study guide

Next couple of lectures 4/23/14Logic of hypothesis testing with Correlations

Interpreting the Correlations and scatterplots

Simple and Multiple Regression

Using correlation for predictions

r versus r2

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)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)

Coefficient of regression will “b” for each variable (like slope)

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)
- 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)

Pop Quiz - 5 Questions

1. What is regression used for?

- Include and example

2. What is a residual? How would you find it?

3. What is Standard Error of the Estimate (How is it related to residuals?)

4. Give one fact about r2

5. How is regression line like a mean?

r2

Writing Assignment - 5 Questions

1. What is regression used for?

- Include and example

Regressions are used to take advantage of relationships

between variables described in correlations. We choose a value

on the independent variable (on x axis) to predict values for

the dependent variable (on y axis).

Writing Assignment - 5 Questions

2. What is a residual? How would you find it?

Residuals are the difference between our predicted y (y’)

and the actual y data points. Once we choose a value on our

independent variable and predict a value for our dependent

variable, we look to see how close our prediction was. We

are measuring how “wrong” we were, or the amount of “error”

for that guess.

Y – Y’

Writing Assignment - 5 Questions

3. What is Standard Error of the Estimate (How is it related to residuals?)

The average length of the residuals

The average error of our guess

The average length of the green lines

The standard deviation of the regression line

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

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 X1 + b2 X2 + b3 X 3 + a

Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

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 X1 + b2 X2 + b3 X 3 + a

Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

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 X1 + b2 X2 + b3 X 3 + a

Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

- Y’ is the dependent variable
- “Success score” is your dependent variable.
- X1 X2 and X3are 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

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.

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.

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.

Here comes Victoria, her scores are as follows:

Prediction line:

Y’ = b1X 1+ b2X 2+ b3X 3+ a

Y’ = 1X 1+ 20X 2- 75X 3+ 700

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

(1)(30)

- 75(2)

+ (20)(8)

+ 700

Y’ =

= 3.812

Y’ = 740

Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

her scores are as follows:

Prediction line:

Y’ = b1X 1+ b2X 2+ b3X 3+ a

Y’ = 1X 1+ 20X 2- 75X 3+ 700

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

(1)(30)

- 75(2)

Y’ =

+ (20)(8)

+ 700

= 3.812

Y’ = 740

Here comes Victor,

his scores are as follows:

We predict

Victor will have a Success Index of 175

- Age = 35
- Niceness = 2
- Harshness= 8

What would we predict his “success index” to be?

Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

(1)(35)

- 75(8)

+ (20)(2)

+ 700

Y’ =

Y’ = 175

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?

See you next time!!

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