Question

1. A new restaurant keeps track of the number of nightly customers at monthly intervals over the course of a year. The restaurant has done very little advertising; most of its publicity is by word of mouth but its number of customers is increasing. The restaurant does not have a seasonal difference in number of customers (for example, no summer crowds).

1. Using the data below, fit each an exponential regression model to the data using Excel.

Month	Nightly customers
0	35
1	41
2	46
3	54
4	66
5	84
6	103
7	117
8	141
9	180
10	222
11	275

1. Write down your regression equation.

2. Enter the regression equation into your calculator and use the table feature to estimate when the restaurant will have 400 people.

3. What does the model predict about the number of customers in 18 months?

4. What does the model predict as time goes on? For example how many customers will be at the restaurant in 300 months (25 years), is this reasonable?

5. What is the growth rate of your regression equation? Find and interpret it.

Answer 1

Performed below regression analysis in excel from the datanalysis tool pack addin in data

Regression output below

So the Regression eqn. is Customers=1.859 + 20.33*Month

Q)when the restaurant will have 400 people.

Customers=1.859 + 20.33*Month

400=1.859 + 20.33*Month

So., Month=19.58392 ~=20 months

So the restaurant will have 400 people after 20 months

Q) model predict about the number of customers in 18 months

Customers=1.859 + 20.33*Month

Customers=1.859 + 20.33*18 =367.799 ~=368

ans=368

Q)For 300 months

Customers=1.859 + 20.33*300 =6100 (Which is not reasonable and hence we need to cap the regression eqn at a particular month based upon the capacity and population)

Q)Growth rate is 20.33 as it is the intercept of month and hence we can interpret as every forthcoming month increases the customers by 20.33 units

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!