A4.pdf - STAT 359\/563 A01(Spring 2018 Assignment 4 Due 1:00pm March 29 1(15 marks One study examined the impact of temperature on the viscosity of

A4.pdf - STAT 359/563 A01(Spring 2018 Assignment 4 Due...

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STAT 359/563 A01 (Spring 2018) Assignment 4: Due 1:00pm, March 29 1. (15 marks) One study examined the impact of temperature on the viscosity of toluene-tetralin blends. The data are given in the following table, where temper- ature is measured in o C and viscosity is in mPa · s. Temperature 24.9 35.0 44.9 55.1 65.2 75.2 85.2 95.2 Viscosity 1.133 0.977 0.853 0.755 0.672 0.602 0.542 0.507 (a) (6 marks) Plot the data and fit the simple linear regression model. Is the linear model a good fit for the data? (Include residual analysis here.) (b) (7 marks) Fit a quadratic model. Present the residual analysis and the fitted model. Also include the scatter plot with fitted quadratic line. (c) (2 marks) What proportion of the variation in viscosity can be explained by the quadratic model in (b)? 2. (15 marks) The file “growth2.csv” gives data on the height of a white spruce tree measured annually for 50 years. Letting Y t (m) denote the height of the tree at year t > 0, we consider describing the growth of the tree over time with a non-linear model Y t = f ( t ) + t ; t i.i.d. N (0 , σ 2 ).
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