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	179	8.4
2	179	8.3
3	174	7.5
4	198	6.3
5	173	7.2
6	178	6.9
7	160	8.3

  
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 rdenominator =  (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 nocorrelation. 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 indirectrelationship. 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)

From the given data, the following Table is calculated:

X	Y	XY	X2	Y2
179	8.4	1503.6	32041	70.56
179	8.3	1485.7	32041	68.89
174	7.5	1305.0	30276	56.25
198	6.3	1247.4	39204	39.69
173	7.2	1245.6	29929	51.84
178	6.9	1228.2	31684	47.61
160	8.3	1328.0	25600	68.89
Total = 1241	52.9	9343.5	220775	403.73

(b)

Value of r_denominator is given by:

(c)

r_numerator is given by:

So,

r = - 244.4/384.7451 = - 0.6352

So,

Answer is:

- 0.6352

(d)

The correlation strength for this problem can be described as strong correlation.

(e)

The correlation direction for this problem can be described as indirect relationship

(f)

The Equation of the Regression Line is:

y = 15.665 - 0.046 x

For y = 8.58, we get:

8.58 = 15.665 - 0.046 x

So,

x = (15.665 - 8.58)/0.046 = 154.0217 = 154 (Round to integer)

So,

Answer is:

154