Statistics Assessment Solutions

Statistics Assessment

Answer 1:
a. Covariance of a sample was calculated using the formula as
COV ( x , y ) =
∑
i=1
n
( xi−x
−
)∗( yi− y
−
)
n−1
Where x
−
and y
−
were the sample means and n was the number of sample
observations.
Hence, sample means were calculated as
x
−
=44
8 =5 .5
y
−
=148
8 =18 . 5
Table 1: Calculation Table for Covariance and Variances
Means
Sl.No 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 0.00 0.00 42.00 192.00 -89.00
X-bar=5.5 Y-bar=18.5
Sample covariance was calculated as COV ( x , y ) =−89
7 =−12. 71 (where n−1=7 )
The joint distribution of experience and salary was negative, implying that the
covariance between the two variables had negative value. This indicated that for
increase in experience, salary was decreasing.

b. Relation between salary and experience was linear but negative in nature. Due to
increase in experience, salary was getting slashed. The coefficient of determination
of 0.982 indicated that experience was able to explain 98.2% variation in salary, in a
linear trend.
Figure 1: Experience-Salary Scatter Plot
c. Pearson’s correlation coefficient between the salary and experience was calculated
as
r xy= Cov ( x , y )
S x S y where Cov ( x , y )was the covariance, Sx and S y were standard
deviations for experience and salary. The values of Sx and S y were calculated as
below using Table 1.
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
Hence,
r xy= Cov ( x , y )
S x S y
= −12. 71
2 . 45∗5 . 24 =−0. 990
The value of the Pearson’s correlation coefficient was highly negative, which
indicated that experience in job and salary were inversely related.
d. The trend of the relation of salary and experience was negative. Probably, the company
was looking for fresh candidates with new ideas. Old employees find it difficult to adapt
to new situations. Hence, company was offering less salary to experienced employees.