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Fundamentals of Business Economics
CHAPTER 10 – INTER-RELATIONSHIPS BETWEEN VARIABLES
10.1 +0.283
n ∑ xy - ∑ x ∑ y
r =
2
2
(n ∑ x -( ∑ x) )(n ∑ y -( ∑ y) )
2
2
2
2
= [10×12,000 – 500 × 200]/√{[10 × 35,000 – 500 ][10 × 9,000 – 200 ]}
= [20,000]/√{[100,000][50,000]}
= 0.283 (3 d.p.)
10.2 A
10.3 +0.98
6d 2
R = 1 – = 1 – (6 × 4,081)/(100 × 9,999) = 1 – 0.0245 = 0.9755
2
n(n – 1)
= 0.98 (to 2dp)
10.4 A and B
Statement C is incorrect: x = 0 is outside the range of the data (extrapolation is
less reliable than interpolation).
Statement D is incorrect: when x increases by $1, y increases by $15 from the
regression equation.
Statement E is incorrect – you need to square the correlation coefficient to get
the coefficient of determination to make such statements.
10.5 0.69
n ∑ xy - ∑ x ∑ y
b = 2
2
(n ∑ x -( ∑ x) )
2
b = [(11 × 13,467) – (440 × 330)]/[(11 × 17,986) – 440 )]
b = 2,937/4,246 = 0.6917 = 0.69
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