SBS200 COMM200 GEOG200 PA200 POL200 or SOC200 Lecture Section 001 Spring 2015 Room 150 Harvill Building 800 850 Mondays Wednesdays amp Fridays Welcome Lab sessions Labs continue ID: 688176
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Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Spring 2015Room 150 Harvill Building8:00 - 8:50 Mondays, Wednesdays & Fridays.
WelcomeSlide2Slide3
Lab sessions
Labs continue this week with Multiple Regression Slide4
Schedule of readingsBefore next exam (Monday May 4th)Please read chapters 10 – 14 Please read Chapters 17, and 18 in Plous
Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions Slide5
Homework due – Monday (April 27th)On class website: Homework worksheet #20Creating multiple choice questions
Extra Credit Opportunity
Please note:
- No class on Friday –
- A morning of rest - Slide6
Next couple of lectures 4/22/15Use this as your study guide
Logic of hypothesis testing with CorrelationsInterpreting the Correlations and scatterplotsSimple and Multiple RegressionSlide7
Homework ReviewSlide8
the hours worked and weekly pay is a strong positive correlation. This correlation is significant, r(3) = 0.92; p < 0.05
The relationship between
+0.92
positive
strong
up
down
6.0857
55.286
y
' = 6.0857x +
55.286
207.43
85.71
.846231 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 $6.09Slide9
400380
360
340
320
300
4
8
5
6
7
Number of Operators
Wait Time
280Slide10
-.73The relationship betweenwait time and number of operators working is negative and
moderate. This correlation is not significant
, r(3) = 0.73;
n.s
.
negative
strong
number of operators increase, wait time decreases
458
-18.5
y'
= -18.5x + 458
365 seconds
328 seconds
.53695 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
Critical r = 0.878
No we do not reject the nullSlide11
3936333027
2421Median Income
Percent of BAs
45 48 51 54 57 60 63 66Slide12
0.8875The relationship betweenmedian income and percent of residents with BA degree is strong and positive. This
correlation is significant,
r(8)
=
0.89;
p <
0.05.
positive
strong
median income goes up so does percent of residents who have a BA degree
3.1819
25% of residents
35% of residents
.78766 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
Percent of residents with a BA degree
10
8
0.0005
y'
=
0.0005x + 3.1819
Critical r = 0.632
Yes we reject the nullSlide13
3027242118
1512Median Income
Crime Rate
45 48 51 54 57 60 63 66Slide14
-0.6293
The relationship between
crime rate and median income is negative and moderate. This
correlation
is not significant
,
r(8)
=
-0.63;
p <
n.s
.
[0.6293 is not bigger than critical of 0.632]
.
negative
moderate
median income goes up, crime rate tends to go down
4662.5
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
Crime Rate
10
8
-
0.0499
y'
= -0.0499x + 4662.5
Critical r = 0.632
No we do not reject the nullSlide15
Multiple regression equations Can use variables to predict behavior of stock market probability of accident amount of pollution in a particular well quality of a wine for a particular year which candidates will make best workers
R
eview Slide16
Y’ = b1 X1 + b2 X2 + b
3 X 3 + a
Measured current workers – the best workers tend to have highest
“success scores”.
(Success scores range from 1 – 1,000)
Try to predict which applicants will have the highest success score.
We have found that these variables predict success:
Age (X
1
)
Niceness (X
2
)
Harshness (X
3
)
According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Both 10 point scales
Niceness (10 = really nice)
Harshness (10 = really harsh)
Success score
= (1)(
Age
) + (20)(
Nice
) + (-75)(
Harsh
) + 700
Y’
= b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ a
Can use variables to predict which candidates will make best workers
R
eview Slide17
Y’ = b1 X1 + b2 X2 + b
3 X 3 + a
According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Success score
= (1)(
Age
) + (20)(
Nice
) + (-75)(
Harsh
) + 700
R
eview Slide18
Y’ is the dependent variable “Success score” is your dependent variable. X1 X2 and X3 are the independent
variables “Age”, “Niceness” and “Harshness” are the independent variables.
Each “b”
is called a
regression coefficient
.
Each “b” shows the change in Y for each unit change in its own X
(holding the other independent variables constant).
a is the Y-intercept
Y’
= b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ a
According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Success score
= (1)(
Age
) + (20)(
Nice
) + (-75)(
Harsh
) + 700
Y’ = b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ a
R
eview Slide19
14-19The Multiple Regression Equation – Interpreting the Regression Coefficientsb1 = The regression coefficient for
age (X1) is
“1”
The
coefficient is
positive
and
suggests a positive correlation between age and success.
As
the
age increases the success score increases. The
numeric value of the regression coefficient provides more information.
If age increases by 1 year and
hold the other two independent variables constant,
we
can
predict a 1 point increase in the success score.
Y’ = b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ a
Success score = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700Slide20
14-20The Multiple Regression Equation – Interpreting the Regression Coefficientsb2 = The regression coefficient for
age (X2
)
is
“20”
The
coefficient is
positive
and
suggests a positive correlation between niceness and success.
As
the
niceness increases the success score increases. The
numeric value of the regression coefficient provides more information.
If the “niceness score” increases by one, and
hold the other two independent variables constant,
we
can
predict a 20 point increase in the success score.
Success score = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y’ = b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ aSlide21
14-21The Multiple Regression Equation – Interpreting the Regression Coefficientsb3 = The regression coefficient for
age (X3
)
is
“-75”
The
coefficient is
negative
and
suggests a negative correlation between harshness and success.
As
the
harshness increases the success score decreases. The
numeric value of the regression coefficient provides more information.
If the “harshness score” increases by one, and
hold the other two independent variables constant,
we
can
predict a 75 point decrease in the success score.
Success score = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y’ = b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ aSlide22
Y’ is the dependent variable “Success score” is your dependent variable. X1 X2 and X3 are the independent
variables “Age”, “Niceness” and “Harshness” are the independent variables.
Each “b”
is called a
regression coefficient
.
Each “b” shows the change in Y for each unit change in its own X
(holding the other independent variables constant).
a is the Y-intercept
Y’
= b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ a
According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula:
Success score
= (1)(
Age
) + (20)(
Nice
) + (-75)(
Harsh
) + 700Slide23
Here comes Victoria, her scores are as follows: Age = 30
Niceness = 8 Harshness
=
2
What would we predict her
“success index” to be?
Y’
=
= 3.812
Prediction line:
Y’
= b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ a
Y’
=
1
X
1
+
20
X
2
- 75
X
3
+ 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
We predict
Victoria will have a
Success Index of 740
Y’
=
740
(1)
(30)
+ (
20)
(8)
-
75
(2)
+ 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700Slide24
Here comes Victor, his scores are as follows:Here comes Victoria,
her scores are as follows:
Age = 30
Niceness = 8
Harshness
=
2
What would we predict her
“success index” to be?
Y’
=
= 3.812
We predict
Victor will have a Success Index of 175
Prediction line:
Y’
= b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ a
Y’
=
1
X
1
+
20
X
2
- 75
X
3
+ 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y’
=
740
(1)
(30)
+ (
20)
(8)
-
75
(2)
+ 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700
Age = 35
Niceness = 2
Harshness
=
8
We predict
Victoria will have a
Success Index of 740
What would we predict
his “success index” to be?
Y’
=
Y’
=
175
(1)
(35)
+ (
20)
(2)
-
75
(8)
+ 700
Y' = (1)(
Age
) + (20)(
Nice
) + (-75)(Harsh) + 700Slide25
We predictVictor will have a Success Index of 175We predictVictoria will have a Success Index of 740
Can use variables to predict which
candidates will make best workers
Who will we hire?Slide26
Thank you!See you next time!!