The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales...

The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales and other potentially relevant variables for that particular restaurant.

Consider the model:
sales_t
=


₀


+


₁

t +


₂

pop_t
+


₃

adv_t
+


₄

adv_t-1
+


_t

where sales_t
= sales in year t,

           pop_t
= size of the population residing within 10 kilometres of the restaurant,

           adv_t
= advertising expenditures in year t, and

           adv_t-1
= advertising expenditures in the previous year.

Based on the sample data, a regression analysis was performed and the results are shown below.

You are required to answer the following questions:

1. Estimate the sample regression equation.


2. What proportion of variation in annual sales is explained by variation in year, population size, advertising expenditure for current year and advertising expenditure for previous year?


3. Construct a 99% confidence interval for From this confidence interval, can you conclude that previous year advertising expenditure influence current year sales?


4. Test at 5% level of significance the hypothesis that year, population size, advertising expenditure for current year and advertising expenditure for previous year jointly influence annual sales.