1. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
Row A 15 14
Row A 13 3 2 1
Row A
Row B 23 20
Row B 19 5 4
3 2 1
Row B
Row C 25 21
Row C 20 6 5 1
Row C
Row D 29 23
Row D 22 8 7 1
Row D
Row E 31 23
Row E 23 9 8 1
Row E
Row F 35 26
Row F 25 11 10 1
Row F
Row G 35 26
Row G 25 11 10 1
Row G
Row H 37 28 27 13
Row H 12 1
Row H 41 29 28 14 1
Row J
Row J 13 41 29
Row K 28 14 13 1
Row K
Row L 33 25
Row L 24 10 9 1
Row L
Row M 21 20 19
Row M 18 4 3 2 1
Row M
Row N 15 1
Row P 15 1
table 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk
Harvill 150
renumbered

2. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2018 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome
11/28/18

3. A note on doodling

4. All remaining homework assignments are available on class website

5. Study Guide for Exam 4 is available on class website
Schedule of readings
Before our fourth and final exam (December 3rd)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

6. Over next couple of lectures 11/26/18
Logic 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)

7. Lab sessions
Pick up past assignments
Labs optional this week

8. 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

9. 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

10. Dustin spends $12 for his Birthday
Angelina Jolie Buys Brad Pitt a $24 million
Heart-Shaped Island for his 50th Birthday
Angelina probably makes this much
Expenses per year
Yearly Income
Dustin probably makes this much
Dustin spent this much
Angelina spent this much
Dustin spends $12
for his Birthday
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. Correlation - the prediction line
- what is it good for?
Prediction line
makes the relationship easier to see
(even if specific observations - dots - are removed)
identifies the center of the cluster of (paired) observations
identifies the central tendency of the relationship (kind of like a mean)
can be used for prediction
should be drawn to provide a “best fit” for the data
should be drawn to provide maximum predictive power for the data
should be drawn to provide minimum predictive error

13. Predicting Restaurant Bill
Prediction line
Y’ = a + b1X1
Cost will be about 95.06
Predicting Restaurant Bill
Cost
Y-intercept
The expected cost for dinner for two couples (4 people) would be $ Cost = Persons
People
If People = 4
Slope
If “Persons” = 4, what is the prediction for “Cost”?
Cost = Persons
Cost = (4)
Cost = = 95.06
If “Persons” = 1, what is the prediction for “Cost”?
Cost = Persons
Cost = (1)
Cost = = 35.18

14. Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (800) Rent = 150 + 840 = 990
Prediction line
Y’ = a + b1X1
Rent will be about 990
Predicting Rent
Cost
Y-intercept
Slope
If SqFt = 800
Square Feet
The expected cost for rent on an 800 square foot apartment is $ Rent = SqFt
If “SqFt” = 800, what is the prediction for “Rent”?
Rent = SqFt
Rent = (800)
Rent = = 990
If “SqFt” = 2500, what is the prediction for “Rent”?
Rent = SqFt
Rent = (2500)
Rent = = 2,775

15. 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”)

16. r2 = Coefficient of determination (“amount of variance accounted for”)
regression coefficient (“b”) or (slope)
What variable are we predicting?
a. Height of Boys in 1990 (cm) b. Age of boys in 1990
c. Both height and age of boys in 1990
Correlation coefficient (“r”)
Coefficient of determination (“r2”)
(“amount of variance accounted for”)
r2 = Coefficient of determination
(“amount of variance accounted for”)

17. Just for fun let’s do the math Y’ = 7.1521 (8) + 64.476 = 122
regression coefficient (“b”) or (slope)
Correlation coefficient (“r”)
Coefficient of determination (“r2”)
(“amount of variance accounted for”)
If a boy is 8-years old how tall would we predict he would be?
Complete prediction “by eye” looking at graph?
a. 40 cm b. 80 cm
c. 120 cm
d. 160 cm
Just for fun let’s do the math
Y’ = (8) = 122

18. Just for fun let’s do the math Y’ = 7.1521 (2) + 64.476 = 78.8
regression coefficient (“b”) or (slope)
Correlation coefficient (“r”)
Coefficient of determination (“r2”)
(“amount of variance accounted for”)
If a boy is 2-years old how tall would we predict he would be? Complete prediction “by eye” looking at graph?
a. 40 cm b. 80 cm
c. 120 cm
d. 160 cm
Just for fun let’s do the math
Y’ = (2) = 78.8

19. regression coefficient (“b”) or (slope)
Correlation coefficient (“r”)
Coefficient of determination (“r2”)
(“amount of variance accounted for”)
What variable are we predicting?
a. Size of state (square miles) b. Number of letters in name of state
c. Both size of state and number of letters

20. Just for fun let’s do the math Y’ = -2,561.5 (7) + 67,884 = 49,953
If a state has 7 letters in the name (like Arizona) how large would we predict the state to be? Complete prediction “by eye” looking at graph?
a. 20,000 square miles b. 30,000 square miles
c. 40,000 square miles
d. 50,000 square miles
Residual is measure of error
for any one data point
y-y’
114,000 – 50,000 =
64,000
114,000
Just for fun let’s do the math
Y’ = -2,561.5 (7) + 67,884 = 49,953

21. regression coefficient (“b”) or (slope)
What variable are we predicting?
a. Size of TV (inches) b. Sales price of TV ($)
c. Both sales price and size of TV
Correlation coefficient (“r”)
Coefficient of determination (“r2”)
(“amount of variance accounted for”)

22. Just for fun let’s do the math
If a TV is 55 inches what would we predict cost to? Complete prediction “by eye” looking at graph?
a. $1,500 b. $1,725
c. $2,000
d. $2,225
Just for fun let’s do the math
Y’ = (55) – = $2,235

23. Just for fun let’s do the math
If a TV is 40 inches what would we predict cost to? Complete prediction “by eye” looking at graph?
a. $1,500 b. $1,725
c. $2,000
d. $2,225
Just for fun let’s do the math
Y’ = (40) – = $1,439

24. What variable are we predicting?
a. Amount of Wine Consumed
b. Death Rate in the Country
c. Both Amount of Wine Consumed and Death Rate

25. Just for fun let’s do the math
If a country consumes an average of 8 liters (per capita) what would we predict death rate from heart disease be? Complete prediction “by eye” looking at graph?
a. 50
b. 75
c. 100
d. 125
Just for fun let’s do the math
Y’ = (8) = 75.6

26. Thank you!
See you next time!!