Question

In: Statistics and Probability

Four factors, each with two levels were studied in a study of the performance of a...

Four factors, each with two levels were studied in a study of the performance of a process: time (A), humidity (B), pressure (C) and the temperature (D). One replicate was run a design 2⁴ and response is presented in the following table.

For this experiment use standard levels for each factor (1,2).

Use MINITAB to set up and analyze the experiment up to 2-level interactions. (i.e. AB, BC, etc…) Note: the response is in not randomized runs. Explain the results!

What factors and interactions are significant?
What are the p-value of interactions A*C, A*D and C*D?

Response
5000
2268
1183
1792
2023
1575
2800
1575
7000
4375
1183
4032
2527
4500
2023
3703

Expert Solution

Here, 4 Factors 2 levels 1 replicate = 16 runs

3 2

To get the answers for the below , you need the data for the time (A), humidity (B), pressure (C) and the temperature (D).

Follow the steps mentioned, once Minitab is installed :

- Type your data in Minitab

- Go to Stat , then DOE, Factorial, Analyze Factorial Design

- Click Terms, and Under Include terms in the model up through order , choose 2 ( since its a 2 level factor)

- Click ok

What factors and interactions are significant?

- Once the Minitab displays the ANOVA table, read the p value against each factors and their interactions to see what factors are significant. P value <0.05 , the conclusion is that the effects are statistically significant.

What are the p-value of interactions A*C, A*D and C*D?

- Check the ANOVA table.

Check the R-Squared to see in the model fits the data well.

Interpretation of the Dependent Variable (Response Variable) (Graphs made in R software)

We don't see any specific structure which shall fit a response model. There is a huge variation in the data points.

QQ Plot

orchestra answered 1 year ago

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