Regression Equations - Tidewater Community College

Report
A guide for analyzing data
MTH 240 – Community College Statistics
Students
Learning Objectives
Linear Equations Review
Equation of the Line
Different Forms of Linear
Equations
Slope
Correlation
Scatter Plots
Regression Equations
Finding the Line of Best Fit
Excel Video Example
Example: The
Unsupervised Student
Scatter Plot
Regression Equation
References
Sarah DiCalogero - Regression Equations
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Review Basic Linear Equations
Forms of Linear Equations
Slope
Correlation
Create Scatter Plots in Excel
Determine Regression Equations in Excel
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Basic Linear Equation:
y
mx
Sarah DiCalogero - Regression Equations
b
4
Regression Line
“Line of Best Fit”
Different formulas convey same information:
^y
^y
b0x
b
b1
y
ax
b
y
a
bx
mx
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Hawkes and Marsh (2004)
Sarah DiCalogero - Regression Equations
Hawkes and Marsh (2004)
6
Relationship between two variables
Hawkes and Marsh (2004)
Hawkes and Marsh (2004)
Hawkes and Marsh (2004)
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Graphs of Points
x – independent/explanatory variable
y – dependent/response variable
Example:
Number
of Bids
28
5
35
6
40
7
43
44
8
9
Price in Dollars vs. Number of Bids
10
Number of Bids
Price in
Dollars
8
6
4
2
0
0
10
20
30
40
50
Price in Dollars
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Sarah DiCalogero - Regression Equations
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Regression Equation
Price in Dollars vs. Number of Bids
10
Positive Slope
Y-intercept value < 0
Correlation
Number of Bids
8
y = 0.2299x - 1.7356
6
4
2
0
0
10
20
30
40
Price in Dollars
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10
50
Click on the image to link to the video
YouTube (2009)
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Question: Does the number of hours a
high school student spends unsupervised
impact their overall grade average?
Hours Unsupervised
Overall Grade Average
0
1.5
2
2.5
3
4.5
5
88
82
76
75
74
69
67
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Hours
Unsupervised
Hours Unsupervised vs.
Overall Grades
Overall Grade
Average
0
1.5
2
2.5
3
4.5
5
88
82
76
75
74
69
67
Overall Grade
100
80
60
40
20
0
0
1
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2
3
4
5
Hours Unsupervised
13
6
Hours Unsupervised vs.
Overall Grades
Overall Grade
100
80
60
y = -4.108x + 86.714
40
20
0
0
1
2
3
4
5
6
Hours Unsupervised
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Hawkes, J., & Marsh, W. (2004). Discovering
Statistics (2nd ed.). Charleston, SC: Hawkes
Publishing Inc..
YouTube. (2009). Plotting A Scatter Plot w/
Trendline in Excel. Retrieved from
http://www.youtube.com/watch?v=nnM7Q6gmUA
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