Sintering VariationObjective: Determine the correlation of a Green Dimn.& Sinter Dimn. (or) Green weight & Green Dimn.
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.
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
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=0Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall
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.
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.
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.
The Coefficient of Determination The coefficient of determination (denoted by R2) is a keyoutput of regression analysis•The coefficient of determination ranges from 0 to 1.•An R2 of 0 means that the dependent variable cannot bepredicted from the independent variable.•An R2 of 1 means the dependent variable can be predictedwithout error from the independent variable.•An R2 between 0 and 1 indicates the extent to which thedependent variable is predictable
Scatterplots Which scatter plots below show a linear trend? Noa) 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
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