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

5. Homework on class website:
Please complete homework worksheet #24
Simple Regression Worksheet
Extended due date: Wednesday, April 19th

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

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. 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
Revisit this slide

10. 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
Revisit this slide

11. 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

12. r2 = The proportion of the total variance in one variable that is
What is r2?
r2 = The proportion of the total variance in one variable that is
predictable by its relationship with the other variable
Examples
If mother’s and daughter’s heights are
correlated with an r = .8, then what amount (proportion or percentage)
of variance of mother’s height is accounted for by daughter’s height?
.64 because (.8)2 = .64

13. r2 = The proportion of the total variance in one variable that is
What is r2?
r2 = The proportion of the total variance in one variable that is
predictable for its relationship with the other variable
Examples
If mother’s and daughter’s heights are
correlated with an r = .8, then what proportion of variance of mother’s height
is not accounted for by daughter’s height?
.36 because ( ) = .36 or
36% because 100% - 64% = 36%

14. If ice cream sales and temperature are correlated with an
What is r2?
r2 = The proportion of the total variance in one variable that is
predictable for its relationship with the other variable
Examples
If ice cream sales and temperature are correlated with an
r = .5, then what amount (proportion or percentage) of variance of ice cream sales is accounted for by temperature?
.25 because (.5)2 = .25

15. If ice cream sales and temperature are correlated with an
What is r2?
r2 = The proportion of the total variance in one variable that is
predictable for its relationship with the other variable
Examples
If ice cream sales and temperature are correlated with an
r = .5, then what amount (proportion or percentage) of variance of ice cream sales is not accounted for by temperature?
.75 because ( ) = .75 or
75% because 100% - 25% = 75%

16. Homework Review

17. 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

18. 400
380
360
Wait Time
340
320
300
280 4 5 6 7 8
Number of Operators

19. -.73
negative
strong
No we do not reject the null

21. -.73
negative
strong
0.878
No we do not reject the null
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
The proportion of total variance of wait time accounted for
by number of operators is 54%.
or 54%
For each additional operator added, wait time will decrease by 18.5 seconds

22. 39 36 33 30 27 24 21
Percent of BAs
Median Income

23. Percent of residents with a BA degree10 8
0.8875
positive
strong
0.632

25. Percent of residents with a BA degree10 8
0.8875
positive
strong
0.632
Yes we reject the null
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

26. 30 27 24 21 18 15 12
Crime Rate
Median Income

27. No we do not reject the null
Crime Rate 10 8
negative
moderate
Critical r = 0.632
No we do not reject the null
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

28. Regression Example
Rory is an owner of a small software company and employs 10 sales staff. Rory send his staff all over the world consulting, selling and setting up his system. He wants to evaluate his staff in terms of who are the most (and least) productive sales people and also whether more sales calls actually result in more systems being sold. So, he simply measures the number of sales calls made by each sales person and how many systems they successfully sold.

29. Do more sales calls result in more sales made?
Regression Example 60 70
Number of
sales calls made
systems sold 10 20 30 40 50
Ava
Emily
Do more sales calls result
in more sales made?
Isabella
Emma
Step 1: Draw scatterplot
Ethan
Step 2: Estimate r
Joshua
Jacob
Dependent
Variable
Independent
Variable

30. Regression Example
Do more sales calls result
in more sales made?
Step 3: Calculate r
Step 4: Is it a significant correlation?

31. Do more sales calls result in more sales made?
Step 4: Is it a significant correlation?
n = 10, df = 8
alpha = .05
Observed r is larger than critical r
(0.71 > 0.632)
therefore we reject the null hypothesis.
Yes it is a significant correlation
r (8) = 0.71; p < 0.05
Step 3: Calculate r
Step 4: Is it a significant correlation?

32. Regression: Predicting sales
Step 1: Draw prediction line
r = 0.71
b = (slope)
a = (intercept)
Draw a regression line
and regression equation
What are we predicting?

33. Regression: Predicting sales
Step 1: Draw prediction line
r = 0.71
b = (slope)
a = (intercept)
Draw a regression line
and regression equation

34. Regression: Predicting sales
Step 1: Draw prediction line
r = 0.71
b = (slope)
a = (intercept)
Draw a regression line
and regression equation

35. Describe relationship Regression line (and equation) r = 0.71
Rory’s Regression: Predicting sales from number of visits (sales calls)
Describe relationship
Regression line (and equation)
r = 0.71
Correlation: This is a strong positive correlation. Sales tend to increase as sales calls increase
Predict using regression line
(and regression equation)
b = (slope)
Slope: as sales calls increase by 1, sales should increase by
Dependent
Variable
Intercept: suggests that we can assume each salesperson will sell at least systems
a = (intercept)
Independent
Variable

36. Regression: Predicting sales
You should sell systems
Step 1: Predict sales for a certain number of sales calls
Madison
Step 2: State the regression equation
Y’ = a + bx
Y’ = x
Joshua
If make one sales call
Step 3: Solve for some value of Y’
Y’ = (1)
Y’ =
What should you expect from a salesperson who makes 1 calls?
They should sell systems
If they sell more  over performing
If they sell fewer  underperforming

37. Regression: Predicting sales
You should sell systems
Step 1: Predict sales for a certain number of sales calls
Isabella
Step 2: State the regression equation
Y’ = a + bx
Y’ = x
Jacob
If make two sales call
Step 3: Solve for some value of Y’
Y’ = (2)
Y’ =
What should you expect from a salesperson who makes 2 calls?
They should sell systems
If they sell more  over performing
If they sell fewer  underperforming

38. Thank you!
See you next time!!