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Linear regression equation between torque and diameter

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4. The torque, T Nm, required to rotate shafts of different diameters, D mm,
on a machine has been tested and recorded below.

D(mm) 6 10 14 18 21 25
T(Nm) 5.5 7.0 9.5 12.5 13.5 16.5

(a) Plot a scatter diagram of the results with diameter of the machine as
the independent variable.

(b) Use the method of least squares to determine the linear regression
equation that relates the torque to the diameter.

(c) Estimate the value of torque required when the diameter is 16 mm.

(d) Calculate the coefficient of correlation between these variables and
comment on your prediction obtained in (c)

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This posting explains how to find Linear regression equation and coefficient of correlation.

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4. The torque, T Nm, required to rotate shafts of different diameters, D mm,
on a machine has been tested and recorded below.
D(mm) 6 10 14 18 21 25
T(Nm) 5.5 7.0 9.5 12.5 13.5 16.5
(a) Plot a scatter diagram of the results with diameter of the machine as
the independent variable.
Solution:
Scatterplot is shown below:

(b) Use the method of least squares to determine the linear regression
equation ...

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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