1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
April 15

2. The
Green
Sheets

3. Schedule of readings Before our fourth and final exam (April 29th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

4. Labs continue this week
Lab sessions
Labs continue this week

5. Project 4 - Two Correlations - Two Regression Analyses

6. Homework Due Date Extended

7. 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”)

8. 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.

9. 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

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

11. 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?

12. 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?

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

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

15. 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

16. 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

17. 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

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

19. Regression: Predicting sales
You should sell systems
Step 1: Predict sales for a certain number of sales calls
Emily
Step 2: State the regression equation
Y’ = a + bx
Y’ = x
If make four sales calls
Step 3: Solve for some value of Y’
Y’ = (4)
Y’ =
What should you expect from a salesperson who makes 4 calls?
They should sell systems
If they sell more  over performing
If they sell fewer  underperforming

20. Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels
Ava
Emma
Isabella
Emily
Madison
What should you expect from each salesperson
Joshua
Jacob
They should sell x systems depending on sales calls
If they sell more  over performing
If they sell fewer  underperforming

21. Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels
=14.7
Difference between
expected Y’ and actual Y
is called “residual”
(it’s a deviation score)
Ava
14.7
How did
Ava do?
Ava sold 14.7 more than expected taking into account how many sales calls she made over performing

22. Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels
=-23.7
Difference between
expected Y’ and actual Y
is called “residual”
(it’s a deviation score)
Ava
-23.7
How did
Jacob do?
Jacob sold fewer
than expected taking into account how many sales calls he
made under performing
Jacob

23. Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels
Ava
Emma
Isabella
Emily
Madison
What should you expect from each salesperson
Joshua
Jacob
They should sell x systems depending on sales calls
If they sell more  over performing
If they sell fewer  underperforming

24. Thank you!
See you next time!!