The document discusses analyzing the correlation between different variables in sintering processes using scatter plots and correlation coefficients. It provides examples of scatter plots with positive, negative, and no correlation and defines the coefficient of correlation (ranging from -1 to 1) and coefficient of determination (ranging from 0 to 1). The document then analyzes the correlation between green dimension and sinter dimension, green weight and dimensions, and green weight and sinter dimension for two sintering machines, finding positive, negative, and no correlation.

1. Sintering Variation
Objective: Determine the correlation of a
Green Dimn.& Sinter Dimn.
(or)
Green weight & Green Dimn.

2. Scatter Plot
• A scatter plot is a graph of a collection of
ordered pairs (x,y).
• The graph looks like a bunch of dots, but some
of the graphs are a general shape or move in a
general direction.

3. The Coefficient of Correlation
• Measures the relative strength of the linear
relationship between two variables (denoted by
r) and Unit-less
• Ranges between –1 and 1
• The closer to –1, the stronger the negative linear
relationship
• The closer to 1, the stronger the positive linear
relationship
• The closer to 0, the weaker any positive linear
relationship

4. Scatter Plots of Data with
Various Correlation Coefficients
Y Y Y
X X X
r = -1 r = -.6 r=0
Y
Y Y
X X X
r = +1 r = +.3 r=0
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

5. Positive Correlation
• If the x-coordinates and the
y-coordinates both
increase, then it is
POSITIVE CORRELATION.
• This means that both are
going up, and they are
related.

6. No Correlation
• If there seems to be
no pattern, and the
points looked
scattered, then it is no
correlation.
• This means the two
are not related.

7. Negative Correlation
• If the x-coordinates and the y-
coordinates have one
increasing and one
decreasing, then it is
NEGATIVE CORRELATION.
• This means that 1 is going up
and 1 is going down, making
a downhill graph. This means
the two are related as
opposites.

8. The Coefficient of Determination
The coefficient of determination (denoted by R2) is a key
output of regression analysis
•The coefficient of determination ranges from 0 to 1.
•An R2 of 0 means that the dependent variable cannot be
predicted from the independent variable.
•An R2 of 1 means the dependent variable can be predicted
without error from the independent variable.
•An R2 between 0 and 1 indicates the extent to which the
dependent variable is predictable

9. Scatterplots
Which scatter plots below show a linear trend?
No
a) Correlation c) Negative e)
Correlation
Positive
Correlation
r = -0.9&R2=0 r = -1&R2=1 r = 1&R2=1
f)
Constant
Correlation
r = 0&R2=0

10. Interval Estimates
for Different Values of x
Prediction Interval
for an individual y,
y given xp
Confidence
Interval for
∧ + b 1x the mean of
y = b0 y, given xp
x
x xp

11. GM6 Sintering Machine
Variation

12. Green Part weight ws Green Part Dimn.
Coefficient of Determination is
0.1882%(0.001882)&Coefficient
of Correlation is-4.33% (-0.0433)
that means No Correlation

13. Green Part Dimn.& Sinter Part Dimn.
Coefficient of Determination is
20.367%(0.2036)&Coefficient of
Correlation is 45.12% (0.4512)
that means Positive Correlation

14. Green Part weight & Sinter Part Dimn.
Coefficient of Determination is
2.451%(0.0245)&Coefficient of
Correlation is -15.45% (-0.1545)
that means No Correlation

15. GM4 Sintering Machine
Variation

16. Green Part weight ws Green Part Dimn.
Coefficient of Determination is
0.289%(0.0245)&Coefficient of
Correlation is -5.37% (-0.537)
that means No Correlation

17. Green Part Dimn.& Sinter Part Dimn.
Coefficient of Determination is
9.053%(0.9053)&Coefficient of
Correlation is -30.089%
(-0.30089) that meansNegative Correlation

18. Sinter Part Dimn & Green Part weight
Coefficient of Determination is
14.495%(0.14495)&Coefficient
of Correlation is -38.0734%
Constant Correlation
(-0.380734) that means