Question 3. [6 pts] The electric power consumed each month (y) by a chemical plant is thought to be related to the average
ambient temperature (x1), the number of operation days in the month (x;), the average product purity (x3), and
the tons of product produced (3:4). The past year’s historical data are available and are presented in the
following table J’ EA E2 E3 ’34
240 25 24 91 100
236 31 21 90 95
290 45 24 8 8 l 10
274 60 25 87 88
301 65 25 91 94
316 72 26 94 99
300 80 25 87 97
296 84 25 86 96
267 75 24 88 l 10
276 60 25 91 105
283 50 25 90 100
261 38 23 89 98 (3.1) Develop the formula to convert natural variables (<2) to coded variables (x). (3.2) Suppose that we will use a first order model without interactions, 3’ 2 Bo +Brx1+B2x2 +33% +B4x4 +5: estimate the parameters B ’s using the least-squares estimation.
(3.3) Estimate the variance of noise, 0:. (3.4) Write down the estimated model. Use this model to predict the monthly power usage when §1=77.8,
§2=25, §3=86.5, and ﬁ4=120. [Note: you can write down a model using either x or :2. However, the values of
inputs given here are the values of natural variables. Don’t forget variable conversion before predicting y]. (3.5) Plot (use a computer software, no hand drawing please) the response surface and its contour plot for X1
and X3.