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Notes on Data Collectionand Analysis
Dale WeberPLTW EDDFall 2009
Things to Consider
Experiment Planning• Replication• Randomization• Blocking
Data Analysis• Strength of “Effects”
– Individual Factors– Factor/Factor Interaction
• Modeling• Linear Regression
Replication
1. Using mean of replicate data gives more precise results
2. Comparing mean to raw data gives an estimate of experimental error
– Standard Deviation of data is commonly used– Also, can identify Outliers
Typically 3 Replicates are considered sufficent
Equal Means2x Variance Outliers
2 close pts- suggests dropping outliers- performing another experiment
Randomization and Blocking
Want to “average out” the impact of extraneous factors
Ex. Weather, pressure variation, cone smoothness, etc.
Compile a list of all experiments to be performed (including replicates)
Perform tests in random orderRoll dice or use computer (Excel –RAND) to generate
random sequence
Strength of Effects
Montgomery, D.C. Design and Analysis of Experiments, 2001.
Effect of A: Average of High A value minus Average of Low A value
Factor/Factor Interaction
Montgomery, D.C. Design and Analysis of Experiments, 2001.
Effect of A at Low B:50 - 20 = 30
Effect of A at High B:12 – 40 = -28
Another way to view it
Since the Effect of A depends on value of B: There is Interaction
Modeling
• Regression Model
y 0 1x 1 2x 2 12x 1x 2 ...
Measured output
Random NoiseCoefficients Mean
Factor Values
Interaction Term
Can add other terms to model:
23 ixx
3214 xxxx and so on.
(Multiple) Linear Regression
• You know Linear Regression from using adding trend-lines to plots in Excel
• For multiple independent variables, need to use LINEST function in spreadsheet
1.Make table of model terms in columns with output in last column:
(Multiple) Linear Regression (2)
2. Enter LINEST Command in blank cell
Measured Data
Model Input Data (Exp
Factor values and combos)
Force const ( to 0?T = No F = Yes
Calculate Fit Statistics
Least Squares Fit Coefficients’s – in reverse
order!
R2 – value(Goodness of
Fit)
(Multiple) Linear Regression (3)
3. Drag LINEST cell and Filli. Drag box needs as many Columns as factors and
factor combos in the model + 1ii. Drag box needs 5 Rows.
4. Press F2 to convert LINEST formula and Drag box to an array.
5. Press CTRL+SHIFT+ENTER to fill
(Multiple) Linear Regression (4)
6. Use Least Squares Model to make predictions
ˆ y ˆ 0 ˆ 1x1 ˆ 2x2 ˆ 12x1x2 ...Note: 1. There is no noise term in the fit model
2. A hat (^) signifies model estimate
ANY QUESTONS?Don’t Forget:- LINEST Help File Handout- Montgomery Handout