Reference no: EM132438616

Problem: The authors of "Mathematical Modeling of Weld Bead Geometry, Quality, and Productivity for Stainless Steel Claddings Deposited by FCAW" (J. Mater. Engr. Perform., 2012: 1862-1872) investigated how y = deposition rate was influenced by x₁ = wire feed rate (W_f , in m/min) and x₂ = welding speed (S, in cm/min). The following 22 observations correspond to the experiment condition where applied voltage was less than 30v:

y: 2.718,   3.881,   2.773,   3.924,   2.740,   3.870   

x₁: 17.0,   10.0,   7.0,   10.0,   7.0,   10.0   

x₂: 30,   30,   50,   50,   30,   30   

y: 2.84,   3.901,   2.204,   4.454,   3.324,   3.319  

x₁: 7.0,   10.0,   5.5,   11.5,   8.5,   8.5   

x₂: 50,   50,   40,   40,   40,   20   

y: 3.423,   3.242,   3.385,   3.420,   3.380,   3.402   

x₁: 8.5,   8.5,   8.5,   8.5,   8.5,   8.5   

x₂: 60,   40,   40,   40,   40,   40,   

y: 3.382,   3.388,   3.398,   3.404   

x₁: 8.5,   8.5,   8.5,   8.5   

x₂: 40,   40,   40,   40   

Required:

a. A least squares fit of y = a + b₁ x₁ + b₂ x₂ to this data gave a = .0558, b₁ = .3749, and b₂ = .0028. What value of deposition rate would you predict when wire feed rate = 11.5 and welding speed = 40? What is the value of the corresponding residual?

b. Residual and total sums of squares are .03836 and 5.1109, respectively. What proportion of observed variation in deposition rate can be attributed to the stated approximate relationship between deposition rate and the two predictor variables?