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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.) 1 165 5.9 2 163 6.1 3 171 6.4 4 179 7.0 5 171 7.4 6 186 7.5 7 178 7.8 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 orindirect 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 #).

The Regression analysis is done as follows:
The sale of lobster depend on the price, thus price is independent variable
Price
Units sold
Sr. No.
x
y
x2
xy
y2
1
5.9
165
34.81
973.5
27,225
2
6.1
163
37.21
994.3
26,569
3
6.4
171
40.96
1094.4
29,241
4
7
179
49
1253
32,041
5
7.4
171
54.76
1265.4
29,241
6
7.5
186
56.25
1395
34,596
7
7.8
178
60.84
1388.4
31,684
0
0
0
0
0
0
0
0
0
0
0
0
Total
48.1
1213
333.83
8364.00
210597.00
Mean
6.87142857
173.29
n
7.00
Slope
b =
8.74
∑(x*y)
8364.00
Y-intercept
a =
113.25
x, mean
6.87
Regression line
Y= 19.5357 + 1.4643*t
y, mean
173.29
Coef. Of cor.
R =
0.793883172
∑(x*x)
333.83
Coef. Of det.
R2 =
0.630250491
∑(y*y)
210597.00
∑x
48.10
83
838.43
∑y
1213.00
10
200.62
Sxy
28.9571429
11
209.36
Sxx
3.31428571
28.95714286
Syy
401.428571
3.314285714
0.63025049
8.737068966
Regression line: Y = 113.25 + 8.74x
Coefficient of regression is given as follows:
https://d2vlcm61l7u1fs.cloudfront.net/media%2Fdcc%2Fdcc04dd9-9c17-4baa-a6d5-3fe6888e1ca7%2FphpEJ7Nf9.png
Coefficient of regression (r) = 0.7938
Coefficient of Determination (squared r) = 0.6302
a) x = independent variable. According to this problem, the ∑x = 48.1
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) = √(3.314)(401.43) = 36.47
c) According to this problem, the correlation of coefficient, r, between the two most pertinent variables is = 0.7983 (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 = strong, r is near to 1
e) According to the instructor’s lecture, the correlation direction between any two variables can be described as direct orindirect relationship. The correlation direction for this problem can be described as relationship. Since r is positive relationship is direct
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 #).
Regression line: Y = 113.25 + 8.74x
Y = 113.25 + 8.74(8.58) = 188
expected #s of lobster sold = 188
 
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