Question

QUESTION 3

1. 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	7.5
   2	179	7.9
   3	168	7.5
   4	198	7.1
   5	169	7.1
   6	179	6.2
   7	158	8.2

     
   a) x = independent variable. According to this problem, the ∑x =  
   
   b) r i s 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 #).

Answer 1

a) x=independent variable

$\sum$ x =$\sum$ price

=SUM(C3:C9)

= 51.5

b. Coefficient of correlation =r=n$\sum$ (xy) -($\sum$ x) *($\sum$ y) /sqrt[n*$\sum$ x^2 -($\sum$x) ^2 ] *[n*$\sum$ y^2 -($\sum$y)^2 ]

The denominator of r=sqrt[n*$\sum$ x^2 -($\sum$x) ^2 ] *[n*$\sum$ y^2 -($\sum$y)^2 ]

=sqrt(17.62 *6824)

=346.7458

c. Correlation coefficient ,r =[7 *9050.2 -51.5*1233] /346.7458

=-148.10 /346.7458

=-0.4271

d.Since the absolute value of r is less than 0.7 ,the correlation strength between two variables price and lobster's sold/day is weak.

e.Since the value of r is negative,this indicates that increase in x would decrease y and vice versa. Hence,there is indirect relationship between x and y.

f. Number of lobsters sold =8.58*I5+I4=165.8644 =166

fac C =8.58*15+14 D A B EF 1 2 Day Regression 7.9 Lobster sold/day(y) Price(x) X^2 ly^2 182 7.5 56.25 33124 179 62.41 32041 168 56.25 28224 198 50.41 39204 7.1 50.41 28561 6.2 38.44 32041 158 8.2 67.24 24964 Intercept Price(x) Coefficients 237.9812713 -8.405221339 7.1 1365 1414.1 1260 1405.8 1199.9 1109.8 1295.6 5/ 169 Number of lobsters 165.8644722 179 7 10 11 Total 12 1233 51.5 381.41 218159 9050.2