The document discusses determining the correlation between different sintering process variables. It provides background on scatter plots, correlation coefficients, and coefficient of determination. The results of analyzing correlations between green part dimensions vs sintered part dimensions, green weight vs dimensions, and other pairings are reported. Positive correlation was found between green and sintered dimensions, while other relationships showed no or negative correlation.

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

16. 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

17. 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