Answer:
A.)
ŷ = 47.07049X + 4435.08375 ;
10084
B.)
y = - 9964.5212 + 4251.34435In(x) ;
10389
C.)
Logarithmic model
Explanation:
Given :
Hours of Operation (X) :
40
44
48
48
60
70
72
90
100
168
Average Revenue Y) :
5958
6662
6004
6011
7250
8632
6964
11097
9107
11498
The best fit Given by a linear model for the data is:
ŷ = 47.07049X + 4435.08375
Average Revenue for 120 hours, X
ŷ = 47.07049(120) + 4435.08375
ŷ = 10083.54255 = 10084
A non-linear model which could be used is a logarithmic model:
General form of a Logarithmic model : y=A+Bln(x)
Equation of best fit :
y = - 9964.5212 + 4251.34435In(x)
Average Revenue for 120 hours, X
y = - 9964.5212 + 4251.34435In(120)
y = - 9964.5212 + 20353.275
y = 10388.754 = 10389
Using the correlation Coefficient value :
Linear mode = 0.8731
Logarithmic model = 0.9084
The logarithmic model is preferred as it has a greater correlation Coefficient value Than the linear model.
