Statistics for Business

STATISTICS FOR BUSINESS
STUDENT ID:
[Pick the date]

Question 1
(a) Computation of covariance
x y x- x bar y - y bar (x- x bar)*(y - y bar)
420 2.8 -105 -0.4 42
610 3.6 85 0.4 34
625 3.75 100 0.55 55
500 3 -25 -0.2 5
400 2.5 -125 -0.7 87.5
450 2.7 -75 -0.5 37.5
550 3.5 25 0.3 7.5
650 3.9 125 0.7 87.5
480 2.95 -45 -0.25 11.25
565 3.3 40 0.1 4
Total
5250 32 371.25
Mean
N= 10, x=5250/10 = 525 ¿ y=32/10 = 3.2
Covariance (Covar x , y )=¿(371.25/10) = 37.13
Computation of correlation coefficient
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(b) The above correlation coefficient of 0.979 needs to be interpreted considering both the
magnitude as well as the sign. The positive sign is indicative of a directly proportional
relationship between the two variables. The magnitude is indicative of the relationship
being strong (Morien,, 2017).
(c) Regression line
y = mx + c
m = r ∗ ൬
σy
σx
൰= 0.979 ∗ ൬0.45
83.67൰= 0.0053
c = y bar − b ∗ x bar = 3.2 − ሺ0.0053 ∗ 525ሻ= 0.4156
y = 0.4156 + 0.0053 x
(d) Scatter displayof x and y
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