Statistics for Business

Running head: STATISTICS FOR BUSINESS 1
Statistics for Business
Student Name
Institution

STATISTICS FOR BUSINESS 2
Question 1
a)
x y XY
420 2.8 1176
610 3.6 2196
625 3.75 2343.75
500 3 1500
400 2.5 1000
450 2.7 1215
550 3.5 1925
650 3.9 2535
480 2.95 1416
565 3.3 1864.5
∑ x =¿ ¿
5250
∑ y=¿ ¿
32
∑ xy =¿ ¿171
71.25
x = 525
y= 3.2
sx = 88.19171
sy = 0.477842
Covariance, Cov(x, y) = ∑ xy−n x y
n−1 = 17171.25−(10∗525∗3.2)
10−1 = 41.25
Correlation coefficient, r = Cov( x , y)
sx sx
= 41.25
88.19171∗0.477842 = 0.97884
b)
Since the correlation coefficient between x and y is 0.97884, then there exists a strong
positive correlation between x and y.
c)
The general form of a least squares line:
Y = a+ bx

STATISTICS FOR BUSINESS 3
b= n∑ xy−∑ x ∑ y
n ∑ ( x2 ) − ( ∑ x )
2 = 10 (17171.25 )−(5250∗32)
10 ( 2826250 )−52502 =0.00530
a= ∑ y−b ∑ x
n = 32−0.00530(5250)
10 = 0.4175
Thus,
y = 0.4175+0.00530x
d)
350 400 450 500 550 600 650 700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
f(x) = 0.01 x + 0.42
R² = 0.96
A scatterplot of y against x
x
y
Question 2
a)
At α =0.05 ,w e need to test the hypothesis:
H0 : b=0
Ha : b ≠0
Where “b” is the coefficient of price
The associated p-value of the coefficient of the price is 0.6019. The observed p-value
(0.6019) is greater than 0.05 (significance level); hence, we fail to reject the null