The manager of a seafood restaurant was asked to establish a pricing policy on l

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

188

7.9

2

155

5.9

3

177

7.9

4

173

7.9

5

171

8.2

6

162

6.6

7

162

7.3

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

188

7.9

2

155

5.9

3

177

7.9

4

173

7.9

5

171

8.2

6

162

6.6

7

162

7.3

Explanation / Answer

Sol:

a) x = independent variable. According to this problem, the x = 51.7

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 = 56.1599

c) According to this problem, the correlation of coefficient, r, between the two most pertinent variables is = 0.7919

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 positive.

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 direct relationship

Lobster Sold/day(y) Price ($/lb.)(x) xbar ybar x-xbar y-ybar (x-xbar)(y-ybar) (x-xbar)^2 (y-ybar)^2 188 7.9 7.385714 169.7143 0.514286 18.2857 9.40407951 0.26449 334.3668 155 5.9 7.385714 169.7143 -1.48571 -14.7143 21.86124151 2.207346 216.5106 177 7.9 7.385714 169.7143 0.514286 7.2857 3.74693351 0.26449 53.08142 173 7.9 7.385714 169.7143 0.514286 3.2857 1.68978951 0.26449 10.79582 171 8.2 7.385714 169.7143 0.814286 1.2857 1.04692751 0.663062 1.653024 162 6.6 7.385714 169.7143 -0.78571 -7.7143 6.06123351 0.617346 59.51042 162 7.3 7.385714 169.7143 -0.08571 -7.7143 0.66122351 0.007347 59.51042 total 1188 51.7 44.47142857 4.288571 735.4286 ybar=sum/n=1188/7=169.714 xbar=sum/n=51.7/7=7.3857 Calculation: corrcoeff=44.47142857/sqrt(4.288571)*(735.4286) r=44.47142857/56.15993 r=0.7919

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