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