Simple Linear Regression – Hypothesis Testing and ...



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 |X1 |X2 |X3 |X4 |

|240 |25 |24 |91 |100 |

|236 |31 |21 |90 |95 |

|270 |45 |24 |88 |110 |

|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 |110 |

|276 |60 |25 |91 |105 |

|288 |50 |25 |90 |100 |

|261 |38 |23 |89 |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 |Cp, kJ/kg-K |

|1000 |1.410 |

|1100 |1.1573 |

|1200 |1.1722 |

|1300 |1.1858 |

|1400 |1.1982 |

|1500 |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.

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