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 22

2. The
Green
Sheets

3. Study Guide for Exam 4 On website
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
Study Guide for Exam 4 On website

4. Are optional and will focus on preparing for Exam 4
Lab sessions
Labs this week
Are optional and will focus on preparing for Exam 4

5. Solutions for
Review Sheet
Available

6. 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”)
Revisit this slide

7. 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.
Revisit this slide

8. 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
Revisit this slide

9. 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
Revisit this slide

10. 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
Revisit this slide

11. 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

12. Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels
Difference between
expected Y’ and actual Y
is called “residual”
(it’s a deviation score)
Ava
14.7
Emma
Isabella
-6.8
Emily
Madison
-23.7
7.9
Joshua
Jacob

13. √ Σx N How do we find the average amount of error in our prediction
Deviation scores
Diallo is 0”
Preston is 2”
Mike is -4”
Step 1: Find error for each value
(just the residuals)
Hunter is -2
Y – Y’
Sound familiar??
Step 2: Find average √
∑(Y – Y’)2
Difference between
expected Y’ and actual Y
is called “residual”
(it’s a deviation score)
n - 2
How would we find our “average residual”? N Σx
The green lines show how
much “error” there is in our
prediction line…how much
we are wrong in our predictions

14. These would be helpful to know by heart – please memorize
Standard error
of the estimate (line) =
These would be helpful to know by heart – please memorize
these formula

15. Standard error of the estimate:
How well does the prediction line predict the predicted variable when using the predictor variable?
Standard error
of the estimate (line)
What if we want to know the “average deviation score”? Finding the standard error of the estimate (line)
Standard error of the estimate:
a measure of the average amount of predictive error
the average amount that Y’ scores differ from Y scores
a mean of the lengths of the green lines
Slope doesn’t give “variability” info
Intercept doesn’t give “variability” info
Correlation “r” does give “variability” info
Residuals do give “variability” info

16. 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

17. 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%

18. 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)

19. Review

20. 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

21. Homework Review

22. 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

23. 400
380
360
Wait Time
340
320
300
280 4 5 6 7 8
Number of Operators

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

25. 39 36 33 30 27 24 21
Percent of BAs
Median Income

26. Percent of residents with a BA degree
Critical r = 0.632
Yes we reject the null
Percent of residents with a BA degree 10 8
0.8875
positive
strong
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

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

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

29. Thank you!
See you next time!!