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 #).

Answer 1

Sol:

	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

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