Question

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

Use the method of least squares to determine the linear regression equation that relates the torque to the diamter. Use 3 decimal places for the figures

D (mm)	1	5	11	14	20	24
T (Nm)	1.8	4.2	7.9	9.6	12.9	15.3

?=___D+ ___Nm

Answer 1

Let D (mm) = X

T(mm) = Y

Therefore the Regression Equation of Y on X is

Where are the Means of X and Y

are the Standard Deviations of X and Y

r is the Correlation Coefficient.

	X	Y
	1	1.8
	5	4.2
	11	7.9
	14	9.6
	20	12.9
	24	15.3
MEANS	12.5000	8.6167
S.Ds	7.9739	4.6631
r	0.9998

Therefore the Regression Equation of Y on X is

NOTE: The values of Means, S.Ds and r has been computed using EXCEL.

PROCEDURE:

After typing the Values in the A and B Columns from A2:A7 and B2:B7.

Put the cursor at the required point. Now Select the FORMULAS from MENU. After Selecting the FORMULAS; Select INSERT FUNCTION (fx) from it. After Selecting INSERT FUNCTION; we will Window. From this window;

*Select AVERAGE to get the Mean; in this fill the cell values A2:A7 in Number1 and click on OK; we will get the Mean of X in the cell A8 and drag this command to right i.e to Cell B8 and enter; automatically we get the Mean of Y.

Select STDEV.P to get the S.D; in this fill the cell values A2:A7 in Number1 and click on OK; we will get the S.D of X in the cell A9 and drag this command to right i.e to Cell B9 and enter; automatically we get the S.D of Y.

Select CORREL to get the CORRELATION COEFFICIENT (r); in this fill the cell values A2:A7 in Array1 and fill the cell values B2:B7 in Array2 and click OK; we will get correlation between X and Y.