Statistics Assessment 1 for STA101 - Statistics for Business

Statistics Assessment 1
Unit: STA101 – Statistics for Business

Answer 1:
a. Sample Covariance between the variables is calculated as COV ( x , y ) =
∑
i=1
n
( xi−x
−
)( yi− y
−
)
n−1 where x
−
and y
−
are the sample means
x
−
= 5+3+7 +9+2+ 4+6+ 8
8 =5 .5
y
−
=20+23+15+11+ 27+21+17+14
8 =18 . 5
Table 1: Covariance Calculation Table
Observation x y Xi-X-bar Yi-Ybar (Xi-X-bar)^2 (Yi-Ybar)^2 (Xi-X-bar)*(Yi-Ybar)
1 5 20 -0.5 1.5 0.25 2.25 -0.75
2 3 23 -2.5 4.5 6.25 20.25 -11.25
3 7 15 1.5 -3.5 2.25 12.25 -5.25
4 9 11 3.5 -7.5 12.25 56.25 -26.25
5 2 27 -3.5 8.5 12.25 72.25 -29.75
6 4 21 -1.5 2.5 2.25 6.25 -3.75
7 6 17 0.5 -1.5 0.25 2.25 -0.75
8 8 14 2.5 -4.5 6.25 20.25 -11.25
Total 44 148 0 0 42 192 -89
Hence, sample covariance is calculated as COV ( x , y ) =−89
7 =−12. 71
The covariance interpreted that the two variables had negative linear relation. This indicated that for
increase in X, Y would decrease linearly, and their directions are opposite (Puccio, Piilo, and

Tumminello, 2016).
b. The two variables are related linearly in a negative manner. From the Figure 1 it is clearly visible that
the relationship is linear (from the trend line) in nature, and with increase in X, Y is observed to
decrease.
Figure 1: X-Y Scatter Plot
c. The Pearson’s correlation coefficient is calculated using the formula as
r xy= Cov ( x , y )
S x S y where Sx and
S y are sample standard deviations for x, and y.
Sx= √ ∑
i=1
n
( xi−x
−
) 2
n−1 = √ 42
7 =2 . 45
S y= √ ∑
i=1
n
( yi− y
−
)
2
n−1 = √ 192
7 =5 .24
So,
r xy= Cov ( x , y )
S x S y
= −12. 71
2 . 45∗5 . 24 =−0. 99
The Pearson’s correlation coefficient is negative, implying that the variables are negatively correlated