Q#2.

(a) Plot the points (35, 9), (49, 15,(21, 7),(39, 11),(15, 5),(28, 8),and (25, 9)

(b) r=n∑ xy−∑ x∑ y

√ [n∑ x2− (∑ x )2 ] [n∑ y2−(∑ y )2 ]=

7 (2150 )−(212 ) (64 )

√ [7 (7222 )−(212 )2 ] [7 (646 )−(64 )2 ]r= 1482

√5610×426= 1482

√2389860=0.96

This value for indicates that a STRONG POSITIVE LINEAR relationship exists between income and health care expenditure.

35 9 315 1225 81

49 15 735 2401 225

21 7 147 441 49

39 11 429 1521 121

15 5 75 225 25

28 8 224 784 64

25 9 225 625 81

∑ x=¿212¿ ∑ y=64 ∑ xy=2150 ∑ x2=7222 ∑ y2=¿646 ¿

(c) r2= (0.96 )2=0.9216This value for the coefficient of determination for income and health care expenditure indicates that 92.16% of the variation in health care expenditure is attributed to income.

(Alternatively: Income is responsible for 92.16% of the variability in health care expenditure)

(d)

b=7 (2150 )−(212 ) (64 )[7 (7222 )−(212 )2 ]

=14825610

=0.26

a=64−(0.27×212 )7

=6.767

=1.27

Thus the equation of the least squares regression line is y=1.27+0.26 x

(e) Let x=40in y=1.27+0.26 x

y=1.27+(0.26×40 )=1.27+10.4=11.67

Thus the health care expenditure for a smoker with an income of 40 thousand dollars is predicted to be 11.67 thousand dollars.

Q#3.

(a) Plasma volume (l) is the dependent variable.(N.B. “Resulting plasma volumedepends on the volume of sweat produced”)

(b) Plot the points (5.0, 2.8), (7.1, 2.9),(7.2, 3.4),(5.6, 2.8),(6.2, 2.6),(5.7, 3.5),(7.0, 3.0) and (6.4, 3.1)

(c) Pearson’s correlation coefficient:

r=n∑ xy−∑ x∑ y

√ [n∑ x2− (∑ x )2 ] [n∑ y2−(∑ y)2 ]r= 8 (151.66 )− (50.2 ) (24.1 )

√ [8 (319.5 )−(50.2 )2 ] [8 (73.27 )−(24.1 )2 ]r= 3.46

√35.96×5.35= 3.46

√192.386=0.25

Coefficient of determination:

r2= (0.25 )2=0.0625

(d) The value for Pearson’s correlation coefficient indicates that a WEAK POSITIVE LINEAR relationship exists between volume of sweat produced and the resulting plasma volume. The value for the coefficient of determination indicates that volume of sweat produced is only responsible for 6.25% of the variation in plasma volume

5.0 2.8 14 25 7.84

7.1 2.9 20.59 50.41 8.41

7.2 3.4 24.48 51.84 11.56

5.6 2.8 15.68 31.36 7.84

6.2 2.6 16.12 38.44 6.76

5.7 3.5 19.95 32.49 12.25

7.0 3.0 21 49 9

6.4 3.1 19.84 40.96 9.61

∑ x=¿50.2 ¿ ∑ y=24.1 ∑ xy=151.66 ∑ x2=319.5 ∑ y2=¿73.27 ¿

(e)

b=8 (151.66 )−(50.2 ) (24.1 )[8 (319.5 )− (50.2 )2 ]

= 3.4635.96

=0.1

a=24.1−(0.1×50.2 )8

=19.088

=2.4

Thus the equation of the least squares regression line is y=2.4+0.1 x

(f) Let x=6.6in y=2.4+0.1 x

y=2.4+(0.1×6.6 )=2.4+0.66=3.06

Thus the plasma volume for a man who produces 6.6 ml of body sweat is predicted to be 3.06 l.

(g) Other variables that could influence plasma volume could be: Weight Water retention Blood pressure levels