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looking to verify my work for corrections if needed.


1) To see if a quadratic model makes

sense, first make a scatter plot of quality vs. pressure. Then check to see which of the following gives a better fit in terms of the amount of variation in quality explained: a linear model, a quadratic model (polynomial of order 2), a power model or an exponential model.


Answer:

Linear Model: y = 0.0233x + 53.323, R² = 0.0121

Quadratic Model: y = 0.0028x2 - 0.3565x + 65.184, R² = 0.0855

Power Model: y=51.537x0.0148, R² = 0.0038

Exponential Model: y=52.992e0.0005x, R² = 0.0156



2) Indicate the proportion of variation in quality explained by each of the models.

Answer: See R² of each above.


3) Indicate What Model you Prefer

Answer: Quadratic Model: y = 0.0028x2 - 0.3565x + 65.184, R² = 0.0855; It has the highest R²


4) Using your quadratic model, what do you predict quality will be if pressure is 58?

Answer: y = 0.0028*58^2 - 0.3565*58 + 65.184 = 53.9262


5)Now create the full quadratic model with both variables. To do so, you need to create 3 new columns in the data set. The first is the temperature squared, the second is the pressure squared and the third is the temperature multiplied by the pressure. These 3 new variables, combined with the original pressure and temperature variables, are the 5 independent variables to be used in the quadratic model. What do you predict quality will be if temperature is 98 and pressure is 51?



Data Relevant for Calculations:


Quality: 56.6 87.6 96.9 81.6 58.2 85 94.8 81.1 58 83.9 97.6 81.7 65.8 91.9 96.9 79.9 66.8 91.8 96.9 81.2 66.4 92.1 97.3 78.9 66.5 90.2 90.4 69.8 65.4 90.7 89.7 71.9 65.4 89.4 91.3 71.6 59.9 79.1 77.4 54.6 59 79.8 79.4 55.3 60 79.5 78.5 55.9 44.9 59.4 56.4 30.3 42.6 60.3 55.8 28.5 42.1 61.3 58.6 30.8


Pressure: 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60 50 53 57 60


Temperature 80 80 80 80 80 80 80 80 80 80 80 80 85 85 85 85 85 85 85 85 85 85 85 85 90 90 90 90 90 90 90 90 90 90 90 90 95 95 95 95 95 95 95 95 95 95 95 95 100 100 100 100 100 100 100 100 100 100 100 100

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