linear regression problem
exx7ely
1. A creep test was performed on a wire where the increase in percent strain (e) over
time (t) as a constant load is applied is measured as follows:
time (min): 1.587 3.088 4.590 6.091 7.592 9.094
% strain: 0.08 0.15 0.20 0.29 0.35 0.42
Determine the linear relation between percent strain and time. What will be the
percent strain: at 12 minutes? [note: e = k t]
2. A source of gamma rays was employed to give measured doses of radiation in an
experiment. However, the dosage varied with position in the apparatus as shown
by the data:
position from base point, x (inch): 0. 0.5 1.0 1.5 2.0 3.0 3.5 4.0
dosage, d (105 rads/hr): 1.90 2.39 2.71 2.98 3.92 4.20 4.56 4.88
Generate the linear equation and calculate the missing dosage level at x = 2.5
Inch
3. By measuring the water flow depth (h) over a rectangular weir of width (B) the
volume flow rates (Q) in a channel can be calculated using the following weir
equation:
Q (ft3/s) = [ Cd ( 2 g ) B ] hn (B, h in ft units)
Determine the values of Cd and n based on the following laboratory test data for a
weir of width 6 inches (g = 32.2 ft/sec2).
[note: ln(Q) = ln[ Cd ( 2 g ) B] + n ln(h)
Q (ft3/min): 161 123 87 56 30 11
h (inch): 12 10 8 6 4 2
4. Andrade’s equation relating viscosity, μ (N.s/m2) with temperature, T (K) for liquids
is given by
(B 1/T ) μ = De
Develop Andrade’s equation for water using the following data:
[note: ln ( μ) = ln (D) + B (1/T) ]
temperature, T (oC): 0 20 40 60 80 100
viscosity, μ (N.s/m2x10-3): 1.787 1.002 0.6529 0.4665 0.3547 0.2818
Estimate the viscosity of water at 30 oC and calculate the percent true error
based on the true value 0.7975x10-3 N.s/m2.
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