Higher Engineering Mathematics

LINEAR REGRESSION 575

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Now try the following exercise.

Exercise 219 Further problems on linear

regression

In Problems 1 and 2, determine the equation

of the regression line ofYonX, correct to 3

significant figures.

1.X 14 18 23 30 50

Y 900 1200 1600 2100 3800

[Y=− 256 + 80. 6 X]

2.X 639152142113

Y 1.3 0.7 2.0 3.7 0.5 2.9 4.5 2.7

[Y= 0. 0477 + 0. 216 X]

In Problems 3 and 4, determine the equations of

the regression lines ofXonYfor the data stated,

correct to 3 significant figures.

3. The data given in Problem 1

[X= 3. 20 + 0. 0124 Y]

4. The data given in Problem 2

[X=− 0. 056 + 4. 56 Y]

5. The relationship between the voltage applied
   to an electrical circuit and the current flowing
   is as shown:

Current (mA) Applied voltage (V)

25

411

615

819

10 24

12 28

14 33

Assuming a linear relationship, determine

the equation of the regression line of applied

voltage,Y, on current,X, correct to 4 signif-

icant figures.

[Y= 1. 142 + 2. 268 X]

6. For the data given in Problem 5, determine
   the equation of the regression line of current

on applied voltage, correct to 3 significant

figures.

[X=− 0. 483 + 0. 440 Y]

7. Draw the scatter diagram for the data given
   in Problem 5 and show the regression lines
   of applied voltage on current and current on
   applied voltage. Hence determine the values
   of (a) the applied voltage needed to give a
   current of 3 mA and (b) the current flowing
   when the applied voltage is 40 volts, assum-
   ing the regression lines are still true outside
   of the range of values given.
   [(a) 7.92 V (b) 17.1 mA]


8. In an experiment to determine the relation-
   ship between force and momentum, a forceX,
   is applied to a mass, by placing the mass on an
   inclined plane, and the time,Y, for the veloc-
   ity to change fromum/s tovm/s is measured.
   The results obtained are as follows:
   Force (N) Time (s)
   11.4 0.56
   18.7 0.35
   11.7 0.55
   12.3 0.52
   14.7 0.43
   18.8 0.34
   19.6 0.31

Determine the equation of the regression line

of time on force, assuming a linear rela-

tionship between the quantities, correct to 3

significant figures.

[Y= 0. 881 − 0. 0290 X]

9. Find the equation for the regression line of
   force on time for the data given in Problem 8,
   correct to 3 decimal places.

[X= 30. 194 − 34. 039 Y]

10. Draw a scatter diagram for the data given in
    Problem 8 and show the regression lines of
    time on force and force on time. Hence find
    (a) the time corresponding to a force of 16 N,
    and (b) the force at a time of 0.25 s, assuming
    the relationship is linear outside of the range
    of values given. [(a) 0.417 s (b) 21.7 N]