The manager of a seafood restaurant was asked to establish a pricing policy on l
ID: 3203670 • Letter: T
Question
The manager of a seafood restaurant was asked to establish a pricing policy on lobster dinners. The manager intends to use the pricing $/LB to predict the lobster sales on each day. The pertinent historical data are collected as shown in the table. Anaswer the following questions.
Day
Lobster Sold/day
Price ($/lb.)
1
182
6.8
2
156
6.1
3
189
5.6
4
179
7.0
5
170
7.5
6
163
6.5
7
162
7.2
a) x = independent variable. According to this problem, the x =
b) r is the coeefficient of correlation. Use the r equation to compute the value of the denominator part of the equation. The value for the r denominator = (in 4 decimal places)
c) According to this problem, the correlation of coefficient, r, between the two most pertinent variables is = (in 4 decimal places).
d) According to the instructor's lecture, the correlation strength between any two variables can be described as strong, weak, or no correlation. The correlation strength for this problem can be described as correlation.
e) According to the instructor's lecture, the correlation direction between any two variables can be described as direct or indirect relationship. The correlation direction for this problem can be described as relationship.
f) Regardless, you were told to use the Associative Forecasting method to predict the expected lobster sale. If the lobster price = $8.58, the expected #s of lobster sold = (round to the next whole #).
Day
Lobster Sold/day
Price ($/lb.)
1
182
6.8
2
156
6.1
3
189
5.6
4
179
7.0
5
170
7.5
6
163
6.5
7
162
7.2
Explanation / Answer
a) According to the problem, the sum of X
= ( 182 + 156 + 189 + 179 + 170 + 163 + 162 ) = 1201
b)
Day
Lobster sold/day, X
Price ($/lb), Y
X.Y
X^2
Y^2
1
182
6.8
1237.6
33124
46.24
2
156
6.1
951.6
24336
37.21
3
189
5.6
1058.4
35721
31.36
4
179
7
1253
32041
49
5
170
7.5
1275
28900
56.25
6
163
6.5
1059.5
26569
42.25
7
162
7.2
1166.4
26244
51.84
Sum =
1201
46.7
8001.5
206935
314.15
We need to find out the value of the denominator of the formula for r as presented in #c
Therefore value of the denominator
= Square root( ( 7 x 206935 – 1201 x 1201) x ( 7 x 314.15 – 46.7 x 46.7))
= Square root (( 1448545 – 1442401) x ( 2199.04 – 2180.89))
= Square root ( 6144 x 18.16 ) = 334.082
c) The correlation coefficient between lobster sold ( X) and Price (Y) is
= (r) =[ nxy – (x)(y) i.e. NUMERATOR / Sqrt([nx2 – (x)2][ny2 – (y)2])] .i.e. DENOMINATOR
r: The correlation coefficient is denoted by the letter r.
n: Number of values. 7 in this case
x: This is the first data variable.
y: This is the second data variable.
: The Sigma symbol (Greek) tells us to calculate the “sum of” whatever is tagged next to it.
The value of r = (-) 0.22812
d)Answer: Weak Correlation (since value is far below from 1 and > 0.1)
e)Correlation direction: Indirect relationship (because of negative correlation, one will move in the direction opposite to where other one is moving)
Day
Lobster sold/day, X
Price ($/lb), Y
X.Y
X^2
Y^2
1
182
6.8
1237.6
33124
46.24
2
156
6.1
951.6
24336
37.21
3
189
5.6
1058.4
35721
31.36
4
179
7
1253
32041
49
5
170
7.5
1275
28900
56.25
6
163
6.5
1059.5
26569
42.25
7
162
7.2
1166.4
26244
51.84
Sum =
1201
46.7
8001.5
206935
314.15
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