An artical compared the thickness of a layer of material with the length of the

Question

An artical compared the thickness of a layer of material with the length of the material.The following data was obtained:

Length (x) Thickness (y)

45 3.20

58 3.40

71 3.47

71 3.55

85 3.60

98 3.70

108 3.80

a. Fit a straight line to the data and determine the line equation.

b. Calculate r2 and determine if the linear relationship between the data seems appropriate.

An artical compared the thickness of a layer of material with the length of the material.The following data was obtained: Length (x) Thickness (y) 45 3.20 3.40 58 3.47 71 3.55 71 85 3.60 3.70 98 108 3.80 a. Fit a straight line to the data and determine the line equation b. Calculate re and determine if the linear relationship between the data seems appropriate.

Explanation / Answer

from above

a)b1 =Sxy/Sxx =0.0088

B0=Ybar-Xbar*bo =2.8559

hence line equation Y=0.0088x+2.8559

b) r2 =S2xy/(SSx*SSy) =0.9615

as value of r2 is approximately near to 1; hence it shows strong linear relationship

x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 45.00 3.20 996.76 0.11 -13.74 3.252917 0.00280022 58.00 3.40 344.90 0.02 -7.16 3.367598 0.00104987 71.00 3.47 31.04 0.00 -4.14 3.482279 0.00015079 71.00 3.55 31.04 0.00 1.25 3.482279 0.00458607 85.00 3.60 71.04 0.00 5.59 3.605782 3.3435E-05 98.00 3.70 459.18 0.03 15.92 3.720464 0.00041876 108.00 3.80 987.76 0.07 28.06 3.80868 7.534E-05 Total 536.00 24.72 2921.71 0.24 25.77 0.00911447

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