The manager of a seafood restaurant was asked to establish a

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

183

7.5

2

179

7.9

3

168

7.3

4

199

7.1

5

169

7.1

6

180

6.1

7

158

8.2

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 #).

Solution

here the manager intends to use the pricing $/LB to predict the lobster sales on each day.

a) here x=independent variable=price ($/lb)

the sum(x)=51.2

b) r is the coefficient of correlation.

r=cov(x,y)/sqrt(var(x)*var(y)) where x=price and y=lobster sold/day

hence the denominator is sqrt(var(x)*var(y))=sqrt(0.39*148.2428)=7.6036 [answer]

c) the corrleation coefficient is r=cov(x,y)/sqrt(var(x)*var(y))

now from part b) sqrt(var(x)*var(y))=sqrt(0.39*148.2428)=7.6036

the covariance between x and y is cov(x,y)=-3.50952

hence r=-3.50952/7.6036=-0.451560313~~-0.4516 [answer] [rounded to 4 decimals]

d) here absolute value of r is below 0.5. hence the correlation is weak

e) here value of r is negative. hence as x increases y decreases or vice versa. hence the relationship is indirect.

f) the regression equation of y on x is

y=233-2.72x where x=price and y=lobster sold/day

put x=$8.58

then y=209.6624~210

hence the number of lobster sold is 210 [answer]