SBS200 Lecture Section 001 Spring 2018 Room 150 Harvill Building 900 950 Mondays Wednesdays amp Fridays Welcome 41118 Lecturers desk Harvill 150 renumbered table ID: 736382
Download Presentation The PPT/PDF document "Introduction to Statistics for the Socia..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Introduction to Statistics for the Social SciencesSBS200 - Lecture Section 001, Spring 2018Room 150 Harvill Building9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome
4/11/18Slide2
Lecturer’s desk
Harvill 150
renumbered
table
Screen
19
5
13
3
Row A
Row B
Row C
Row D
Row E
Row F
Row H
Row J
Row K
Row L
Row M
Row N
Row P
Row M
Row E
Row D
Row C
Row B
Row A
Row E
Row C
Row B
Row A
20
6
22
8
23
9
25
24 23 22 21 20 19 18 17 16 15 14 13 12
27
28
24
18
4
15
1
15
1
Screen
Projection Booth
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
15
14
23
20
21
25
Row D
23
29
23
31
Row
F
10
9 8 7 6 5 4 3 2
11
26
35
34 33 32 31 30 29 28 27
Row
G
25
24 23 22 21 20 19 18 17 16 15 14 13 12
Row G
10
9 8 7 6 5 4 3 2
11
26
35
34 33 32 31 30 29 28 27
Row F
Row G
Row H
12
11 10 9 8 7 6 5 4 3 2
28
37
36 35 34 33 32 31 30 29
Row H
13
26 25 24 23 22 21 20 19 18 17 16 15 14
Row J
13
12 11 10 9 8 7 6 5 4 3 2
14
27 26 25 24 23 22 21 20 19 18 17 16 15
29
41
40 39 38 37 36 35 34 33 32 31 30
Row K
13
12 11 10 9 8 7 6 5 4 3 2
28
14
27 26 25 24 23 22 21 20 19 18 17 16 15
29
41
40 39 38 37 36 35 34 33 32 31 30
Row L
9
8 7 6 5 4 3 2
10
23 22 21 20 19 18 17 16 15 14 13 12 11
25
33
32 31 30 29 28 27 26
Row M
21
20
19
18 17 16 15 14 13 12 11 10 9 8 7 6
19 18 17 16 15 14 13 12 11 10 9 8 7
21 20 19 18 17 16 15 14 13 12 11 10 9
22 21 20 19 18 17 16 15 14 13 12 11 10
17 16 15 14 13 12 11 10 9 8 7 6 5
14 13 12 11 10 9 8 7 6 5 4 3 2
14 13 12 11 10 9 8 7 6 5 4 3 2
3
2
1
2
1
12
11 10 9 8 7 6 5 4
30 29 28 27 26 25 24
28 27 26 25 24
24 23 22
7 6 5 4 3 2
6 5 4 3 2
4 3 2
3 2
1
1
1
1
1
1
1
1
1
1
4
5
7
8
22 21
Row L
Left handed deskSlide3Slide4
Before our fourth and final exam (April 30th
)
OpenStax
Chapters
1 –
13
(Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions
Schedule of readingsSlide5
Lab sessions
Project 4
This weekSlide6
Project 4
- Two Correlations
- Two
R
egression
A
nalyses
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 analysisSlide7Slide8
Correlation matricesWe want to predict home price - What do we care about?
We measured the following characteristics of 150 homes
recently sold
Price
Square Feet
Number of Bathrooms
Lot Size
Median Income of Buyers Slide9
Correlation matricesWhat do we care about?Slide10
Correlation matricesWhat do we care about?Slide11
Correlation matricesWhat do we care about?Slide12
Critical r value from tabledf
= # pairs - 2
df
= 148 pairs
α
= .
05
Critical value
r
(148)
= 0.195Slide13
Correlation matricesWhat do we care about?
Critical value from table
r
(148)
= 0.195Slide14
+0.9199
3
0.878Slide15Slide16
+0.9199
3
0.878
Yes
Yes
The relationship
between the hours worked
and weekly
pay is
a strong positive correlation.
This
correlation is
significant, r(3) = 0.92; p < 0.05Slide17
-0.73
3
0.878
No
No
The relationship between wait time and number of
operators working is negative and strong, but not
reliable enough to reach significance.
This
correlation is
not significant
, r(3)
= -0.73
;
n.s
.
3Slide18
We are measuring 9 studentsSlide19Slide20
4.0
3.0
2.0
1.0
0 1 2 3 4
High School GPA
GPA
r(7)
=
0.50
r(7)
=
+ 0.911444123
0 200 300 400 500 600
SAT (Verbal)
GPA
r(7) = + 0.80
r(7)
=
+ 0.616334867
SAT (Mathematical)
GPA
r(7)
= +
0.80
r(7) = + 0.487295007
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
0 200 300 400 500 600
Critical r = 0.666
Reject Null
r is significant
Do not reject
n
ull
r is not significant
Do not reject
n
ull
r is not significantSlide21
4.0
3.0
2.0
1.0
0 1 2 3 4
High School GPA
GPA
r(7)
=
0.50
r(7)
=
+ 0.911444123
0 200 300 400 500 600
SAT (Verbal)
GPA
r(7) = + 0.80
r(7)
=
+ 0.616334867
SAT (Mathematical)
GPA
r(7)
= +
0.80
r(7) = + 0.487295007
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
0 200 300 400 500 600Slide22
4.0
3.0
2.0
1.0
0 1 2 3 4
High School GPA
GPA
r(7)
=
0.50
r(7)
=
+ 0.911444123
0 200 300 400 500 600
SAT (Verbal)
GPA
r(7) = + 0.80
r(7)
=
+ 0.616334867
SAT (Mathematical)
GPA
r(7)
= +
0.80
r(7) = + 0.487295007
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
0 200 300 400 500 600Slide23
4.0
3.0
2.0
1.0
0 1 2 3 4
High School GPA
GPA
r(7)
=
0.50
r(7)
=
+ 0.911444123
0 200 300 400 500 600
SAT (Verbal)
GPA
r(7) = + 0.80
r(7)
=
+ 0.616334867
SAT (Mathematical)
GPA
r(7)
= +
0.80
r(7) = + 0.487295007
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
0 200 300 400 500 600Slide24
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
Dependent
Variable
Dependent
Variable
Independent
Variable
Independent
Variable
What are we predicting?
What are we predicting?Slide25
Correlation - What do we need to define a line
Expenses
per year
Yearly
Income
Y-intercept =
“a”
(
also
“
b
0
”)
Where the line crosses the Y axis
Slope =
“b”
(
also
“
b
1
”)
How steep the line is
If you spend this much
If you probably make 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 variableSlide26
Angelina Jolie Buys Brad Pitt a
$24 million Heart-Shaped
Island for his 50th Birthday
Expenses
per year
Yearly
Income
Angelina spent this
much
Angelina probably makes
this much
Dustin spends $12
for his Birthday
Dustin spent this
much
Dustin probably makes
this much
Revisit this slideSlide27
Assumptions Underlying Linear RegressionThese Y values are normally distributed. The means
of these normal distributions of Y values all lie on the straight line of regression.
For each value of
X
, there is a group
of
Y
values
The
standard deviations
of these normal distributions are equal.
Revisit this slideSlide28
Correlation - the prediction line 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
- what is it good for?Slide29
Predicting Restaurant BillThe expected cost for dinner for two couples (4 people) would be $95.06
Cost = 15.22 + 19.96 Persons
If
“Persons”
= 4, what is the prediction for
“Cost”
?
Cost = 15.22 + 19.96 Persons
Cost = 15.22 + 19.96 (4)
Cost = 15.22 + 79.84 = 95.06
Prediction line
Y’ =
a
+ b
1
X1
Y-intercept
Slope
If “Persons”
= 1, what is the prediction for “Cost”?
Cost = 15.22 + 19.96 Persons
Cost = 15.22 + 19.96 (1)Cost = 15.22 + 19.96 = 35.18
People
Cost
If People = 4
Cost will be about 95.06Slide30
Predicting RentThe expected cost for rent on an 800 square foot apartment is $990 Rent = 150 + 1.05 SqFt
If
“SqFt
”
= 800, what is the prediction for
“Rent”
?
Rent = 150 + 1.05 SqFt
Rent = 150 + 1.05 (800)
Rent = 150 + 840 = 990
Prediction line
Y’ =
a
+ b1X1
Y-intercept
Slope
Square Feet
Cost
If SqFt = 800
Rent will be about 990
If
“
SqFt
”
= 2500, what is the prediction for
“Rent”
?
Rent = 150 + 1.05
SqFt
Rent = 150 + 1.05 (2500)
Rent = 150 +
2625
= 2,775Slide31
Thank you!See you next time!!