Download b - Interpersonal Research Laboratory

Practice
Norm
Alcohol
X
6
Nose Touches
Y
5
Cliff
8
1
Sam
4
4
Woody
2
9
Practice
Norm
Cliff
Sam
Woody

Alch Nose
X
Y
6
5
8
1
4
4
2
9
X
2
Y
2
XY
Practice
Norm
Cliff
Sam
Woody

Alch Nose
X
Y
6
5
8
1
4
4
2
9
20
19
X
2
36
64
16
4
120
Y
2
25
1
16
81
123
XY
30
8
16
18
72
Practice
(4) 72
20
r=
(4) 120
20
19
(4)123
X = 20
X2 = 120
Y = 19
Y2 = 123
XY = 72
N=4
19
Practice
-9220
r=
(4) 120
20
19
(4)123
X = 20
X2 = 120
Y = 19
Y2 = 123
XY = 72
N=4
19
Practice
-9220
r=
80
19
131
X = 20
X2 = 120
Y = 19
Y2 = 123
XY = 72
N=4
Practice
-9220
-.90 =
80
102.37
19
131
X = 20
X2 = 120
Y = 19
Y2 = 123
XY = 72
N=4
Remember this:
Statistics Needed
• Need to find the best place to draw the
regression line on a scatter plot
• Need to quantify the cluster of scores
around this regression line (i.e., the
correlation coefficient)
Regression allows us to predict!
12
Happiness
10
8
.
6
4
. . .
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2
0
2
4
6
Hours Slept
8
10
Straight Line
Y = mX + b
Where:
Y and X are variables representing scores
m = slope of the line (constant)
b = intercept of the line with the Y axis
(constant)
Excel Example
That’s nice but. . . .
• How do you figure out the best values to
use for m and b ?
• First lets move into the language of
regression
Straight Line
Y = mX + b
Where:
Y and X are variables representing scores
m = slope of the line (constant)
b = intercept of the line with the Y axis
(constant)
Regression Equation
Y = a + bX
Where:
Y = value predicted from a particular X value
a = point at which the regression line intersects
the Y axis
b = slope of the regression line
X = X value for which you wish to predict a Y
Practice
• Y = -7 + 2X
• What is the slope and the Y-intercept?
• Determine the value of Y for each X:
• X = 1, X = 3, X = 5, X = 10
Practice
• Y = -7 + 2X
• What is the slope and the Y-intercept?
• Determine the value of Y for each X:
• X = 1, X = 3, X = 5, X = 10
• Y = -5, Y = -1, Y = 3, Y = 13
Finding a and b
• Uses the least squares method
• Minimizes Error
Error = Y - Y
 (Y - Y)2 is minimized
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12
10
Smile
8
6
4
2
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.
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0
1
2
3
Talk
4
5
Error = Y - Y
 (Y - Y)2 is minimized
12
10
Error = 1
Smile
8
6
4
2
.
Error = .5
.
Error = 0
.
Error = -.5
.
.
Error = -1
0
1
2
3
Talk
4
5
Finding a and b
• Ingredients
• r value between the two variables
• Sy and Sx
• Mean of Y and X
b
b=
r = correlation between X and Y
SY = standard deviation of Y
SX = standard deviation of X
a
a = Y - bX
Y = mean of the Y scores
b = regression coefficient computed previously
X = mean of the X scores
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
r = .88
Jerry
Smile
Y
9
Talk
X
5
Elan
2
1
George
5
3
Newman
4
4
Kramer
3
2
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
r = .88
.
12
10
Smile
8
6
4
2
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0
1
2
3
Talk
4
5
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
b=
r = .88
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
2.41
1.50
b = .88 1.41
r = .88
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
r = .88
b = 1.5
a = Y - bX
Mean Y = 4.6; SY = 2.41
Mean X = 3.0; SX = 1.41
r = .88
b = 1.5
0.1 = 4.6 - (1.50)3.0
Regression Equation
Y = a + bX
Y = 0.1 + (1.5)X
Y = 0.1 + (1.5)X
.
12
10
Smile
8
6
4
2
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0
1
2
3
Talk
4
5
Y = 0.1 + (1.5)X
X = 1; Y = 1.6
.
12
10
Smile
8
6
4
2
..
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.
.
0
1
2
3
Talk
4
5
Y = 0.1 + (1.5)X
X = 5; Y = 7.60
.
.
12
10
Smile
8
6
4
2
..
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.
.
0
1
2
3
Talk
4
5
Y = 0.1 + (1.5)X
.
.
12
10
Smile
8
6
4
2
..
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0
1
2
3
Talk
4
5
Practice
Mean Y = 14.50; Sy = 4.43
Mean X = 6.00; Sx= 2.16
r = -.57
Aggression Happiness
Y
X
Mr. Blond
10
9
Mr. Blue
20
4
Mr. Brown
12
5
Mr. Pink
16
6
Mean Y = 14.50; Sy = 4.43
Mean X = 6.00; Sx= 2.16
b=
r = -.57
Mean Y = 14.50; Sy = 4.43
Mean X = 6.00; Sx= 2.16
4.43
-1.17
b =-.57 2.16
r = -.57
Mean Y = 14.50; Sy = 4.43
Mean X = 6.00; Sx= 2.16
a = Y - bX
b = -1.17
Mean Y = 14.50; Sy = 4.43
Mean X = 6.00; Sx= 2.16
21.52= 14.50 - (-1.17)6.0
b = -1.17
Regression Equation
Y = a + bX
Y = 21.52 + (-1.17)X
Y = 21.52 + (-1.17)X
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22
12
20
Aggression
10
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18
8
16
6
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14
4
12
2
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10
0
1
2
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4
5
6
Happiness
7
8
9
10
Y = 21.52 + (-1.17)X
22
12
20
Aggression
10
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18
8
16
6
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14
4
12
2
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10
0
1
2
3
4
5
6
Happiness
7
8
9
10
Y = 21.52 + (-1.17)X
22
12
20
Aggression
10
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.
.
18
8
16
6
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14
4
12
2
. .
10
0
1
2
3
4
5
6
Happiness
7
8
9
10
Y = 21.52 + (-1.17)X
22
12
20
Aggression
10
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.
.
18
8
16
6
.
14
4
12
2
. .
10
0
1
2
3
4
5
6
Happiness
7
8
9
10