Tools>> Data analysis>> Regression (Correlation)
Simple Linear Regression
What is it?
Determines if Y
depends on X and
provides a math
equation for the
y
relationship
Step 2: Analysis via EXCEL
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.85
R Square
0.72
Adjusted R Square 0.71
Standard Error
194.60
Observations
25
ANOVA
Regression Residual Total
run
axis.
b
0
X
A simple linear relationship can be described mathematically by
Y = mX + b
Simple Linear Regression
slope =
rise run
=
(6 - 3)
1
=
(10 - 4)
2
Y
rise
5
run intercept = 1
(continuous data)
x
Does Y depend on X? Which line is correct?
Examples:
Process conditions and product properties
Sales and advertising budget
4
Simple Linear Regression
• “Regression” provides a functional relationship (Y=f(x)) between the variables; the function represents the “average” relationship.
• “Correlation” tells us the direction and the strength of the relationship.
Is there a Relationship Between the Variables?
What Direction is the Relationship?
How Strong is the Relationship?
High
... .
Y.. . . ..
. . .. .
Low
.. . .
Rent
Step 1: Scatter plot
2500 2300 2100 1900 1700 1500 1300 1100 900 700 500
500 700 900 1100 1300 1500 1700 1900 2100
Size
Scatter plot suggests that there is a ‘linear’ relationship between Rent and Size
Low
High
X
Simple Linear Regression
Is there a Relationship Between the Variables?
What Direction is the Relationship?
How Strong is the Relationship?
High
df
SS
MS
F Significance F
1
2268777 2268777 59.91376 7.51833E-08
TheTahneaalnyasliysssistasrtatsrtswwitihthaa SSccaatttteerrPPloltootfoYf Yvs vXs X.
Regression and Correlation
Excel will do Regression analysis and Correlation analysis:
0
X
0
5
10
Y = 0.5X + 1
Simple regression example
A n a g e n tf o ra r e s id e n tia lr e a le s ta te c o m p a n y in a la r g e c ity w o u ld lik e to p r e d ic tth e m o n th ly r e n ta lc o s tf o ra p a r tm e n ts b a s e d o n th e s iz e o fth e a p a r tm e n ta s d e f in e d b y s q u a r e f o o ta g e .A s a m p le o f2 5 a p a r tm e n ts in a p a r tic u la rr e s id e n tia ln e ig h b o r h o o d w a s s e le c te d to g a th e rth e in f o r m a tio n .
... .
?
Y.. .
. ..
?
. . .. .
Low
.. . . ?
Low
gression
m = slope =
rise run
Y
rise
b = Y intercept
= the Y value
at point that
the line
intersects Y
Regression Analysis
Chapter 11
Regression and Correlation
Techniques that are used to establish whether there is a mathematical relationship between two or more variables, so that the behavior of one variable can be used to predict the behavior of others. Applicable to “Variables” data only.