Page 290 - F2 - MA Integrated Workbook STUDENT 2018-19

Chapter 12

Test your understanding 2

The equation of a straight line for the above data would be:

y = 2.45 + 0.30x

n∑xy – ∑x∑y (6 × 7) – (1 × 15) 27
b = ——————— = ———————————— = ——— = 0.30
2
2
n∑x – (∑x) (6 × 15) − 1 2 89
a = y − b x = (15 ÷ 6) – 0.30 × (1 ÷ 6) = 2.45
̅
̅

Test your understanding 3

The correlation coefficient to two decimal places is: 0.86

Using the formula
(12 × 124,258) – (802 × 1,850)

r = ——————————————————— = -0.86
2
2
√ ((12 × 53,792) − 802 )((12 × 287,868) – 1,850 )

Test your understanding 4

A

The coefficient of determination = r 2

2
2
r = 0.8 = 0.64. This suggests that 64% of the changes in y can be explained
by the changes in x.

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