2k Factorial Design k=2 Ex:.

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2k Factorial Design k=2 Ex:

Assuming a model containing 2 main effects and interaction Assuming a model containing 2 main effects and interaction. Calculate 3 effects. Sketch the interaction plot and interpret the graph. Write hypothesis regarding main effects and interaction. Do ANOVA and test for interaction (α = 0.05). Give conclusion. Test for main effects and give final conclusion regarding the importance of all these effects. Write the least squares fitted model using only significant terms. Use the model to predict the response when x1=-1 and x2=-1.

2k Factorial Design k=3

Estimate the factor effects. Which effects appear to be large? Use the analysis of variance to confirm your conclusions for part (a). Write down a regression model for predicting tool life (in hours) based on the results of this experiment. Analyze the residuals. Are there any obvious problems?

Factors B, C, and the AC interaction appear to be large (significant).

The analysis of variance confirms the significance of factors B, C, and the AC interaction.

There is nothing unusual about the residual plots.

Simple Linear Regression Ex:

Multiple Linear Regression Ex: Write fitted multiple linear regression model. Find the residual value of third observation. What is the estimate of Find a 95% CI on Test the significance of regression. Besides write hypotehsis for this test. Calculate the coefficient of multiple determination andjusted coefficient of multiple determination. Interpret the results. Check the model adequacy.

In the following table x1,x2, and y values corresponding to a regression analysis problem are given.