advertisement

Multiple Linear Regression, Interpolation, and Numerical Integration Homework #8 CIVL 3103 Due Tuesday, December 2 1. The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature, x1, the number of days in the month x2, the average product purity, x3, and the tons of product produced, x4. The past year’s historical data are available and are presented in the table below. a. Fit a multiple linear regression model to these data. b. Perform a residuals analysis using graphical methods discussed in class (you do not have to plot a normal curve on the histogram of your residuals). c. Test for the significance of the regression at α = 0.05. d. Use the t-test to assess the contribution of each regressor to the model. Using α= 0.05, what conclusions can you draw? Y 240 236 270 274 301 316 300 296 267 276 288 261 X1 25 31 45 60 65 72 80 84 75 60 50 38 X2 24 21 24 25 25 26 25 25 24 25 25 23 X3 91 90 88 87 91 94 87 86 88 91 90 89 X4 100 95 110 88 94 99 97 96 110 105 100 98 2. Consider the data in the table below. Use interpolation to find the value of the constant-pressure specific heat (Cp) at a temperature of 1238 K. Use a first order, second order, and third order polynomial. Which polynomial do you think is most appropriate for interpolation of this data? Explain your answer. T, K 1000 1100 1200 1300 1400 1500 Cp, kJ/kg-K 1.410 1.1573 1.1722 1.1858 1.1982 1.2095 3. Evaluate the following integral using both the Trapezoid and Simpson’s 1/3 rule with n = 1, 2, 4, and 8 subintervals for Trapezoid and n = 2, 4, and 8 subintervals for Simpson’s rule. Compare these results to the exact solution. 10 (5x 0 4 4 x3 2 x 3)dx