Resource Lesson
Linear Regression and Data Analysis Methods
Printer Friendly Version
When you enter your data from an experiment in an EXCEL spreadsheet, EXCEL will provide you with a regression line. This is a line of best fit or trend line. It approximates the best linear representation for the data which you have entered. In some cases, none of your data points may actually fall on the line; while in others, the line will pass through practically every data point. A statistical method of determining the precision of your data is the correlation coefficient, R
^{2}
. The closer its value is to 1.000, the better the internal consistency within your data.
The equation of this regression line is
d = 2.5t + 6
The correlation coefficient is 0.9833 which is acceptable but would have been better had points 2 and 5 deviated less from the line.
The equation of this regression line is
P = 0.37T - 1
The correlation coefficient of 1.0000 is phenomenal! Notice that the extrapolated line almost passes through T = 0 K, the definition of Absolute Zero.
Formulas and trend line equations
Another aspect of regression lines is the relationship between their equations and the theoretical equations for the physical quantities being graphed.
In the case of the first graph,
d = 2.5t + 6
, the physics behind this behavior states that "distance" equals "rate" times "time;" that is,
d = rt
. Therefore, when the two equations are compared, the coefficient of
t
must represent the rate, or 2.5 m/sec.
d
=
r
t
d
=
2.5
t
+ 6
Thus, on the average, the object moved 2.5 meters each second. The significance of the y-axis intercept is the object's initial position. That is, when time t = 0 sec the object started at a position 6 meters above the "origin."
In the case of the second graph,
P = 0.37T - 1
. The physics behind this behavior is the ideal gas law which states that
PV = nRT
; where,
P
is the pressure in Pascals,
V
is the volume in m
^{3}
,
T
is the temperature in Kelvin, and
n
is the number of moles present in the sample. Solving for
P
reveals that
P = (nR/V) T
. Comparing this with the equation of our line shows that the numerical value of the slope equals the expression nR/V.
PV = nRT
P
= (
nR/V
)
T
P
=
0.37
T
- 1
Since our formula demands that pressure be measured in Pa, and our data is measured in kPa, we must convert 0.37 kPa to 0.37 x 10
^{3}
Pa or 370 Pa. Setting this equivalent numerical value for the slope equal to the expression nR/V yields the following expression for
V
.
370 = nR/V
370 V = nR
V = nR/370
If we now substitute in that 1 mole was present and R equals 8314 J/mole K, we can discover that the volume of gas present was
V = nR/370
V = (1)(8314)/(370)
V = 22.5 m
^{3}
Related Documents
Lab:
Labs -
2-Meter Stick Readings
Labs -
Acceleration Down an Inclined Plane
Labs -
Addition of Forces
Labs -
Circumference and Diameter
Labs -
Cookie Sale Problem
Labs -
Density of a Paper Clip
Labs -
Determining the Distance to the Moon
Labs -
Determining the Distance to the Sun
Labs -
Eratosthenes' Measure of the Earth's Circumference
Labs -
Home to School
Labs -
Indirect Measurements: Height by Measuring The Length of a Shadow
Labs -
Indirect Measures: Inscribed Circles
Labs -
Inertial Mass
Labs -
Introductory Simple Pendulums
Labs -
Lab: Rectangle Measurements
Labs -
Lab: Triangle Measurements
Labs -
Marble Tube Launcher
Labs -
Quantized Mass
Labs -
The Size of the Moon
Labs -
The Size of the Sun
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Basic Trigonometry
RL -
Basic Trigonometry Table
RL -
Curve Fitting Patterns
RL -
Dimensional Analysis
RL -
Metric Prefixes, Scientific Notation, and Conversions
RL -
Metric System Definitions
RL -
Metric Units of Measurement
RL -
Potential Energy Functions
RL -
Properties of Lines
RL -
Properties of Vectors
RL -
Significant Figures and Scientific Notation
RL -
Vector Resultants: Average Velocity
RL -
Vectors and Scalars
Review:
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Puppy Love
APP -
The Dognapping
APP -
The Pool Game
APP -
War Games
CP -
Inverse Square Relationships
CP -
Sailboats: A Vector Application
CP -
Satellites: Circular and Elliptical
CP -
Tensions and Equilibrium
CP -
Vectors and Components
CP -
Vectors and Resultants
CP -
Vectors and the Parallelogram Rule
WS -
Calculating Vector Resultants
WS -
Circumference vs Diameter Lab Review
WS -
Data Analysis #1
WS -
Data Analysis #2
WS -
Data Analysis #3
WS -
Data Analysis #4
WS -
Data Analysis #5
WS -
Data Analysis #6
WS -
Data Analysis #7
WS -
Data Analysis #8
WS -
Density of a Paper Clip Lab Review
WS -
Dimensional Analysis
WS -
Frames of Reference
WS -
Graphical Relationships and Curve Fitting
WS -
Indirect Measures
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
Mastery Review: Introductory Labs
WS -
Metric Conversions #1
WS -
Metric Conversions #2
WS -
Metric Conversions #3
WS -
Metric Conversions #4
WS -
Properties of Lines #1
WS -
Properties of Lines #2
WS -
Scientific Notation
WS -
Significant Figures and Scientific Notation
TB -
Working with Vectors
TB -
Working with Vectors
REV -
Math Pretest for Physics I
PhysicsLAB
Copyright © 1997-2017
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton