Reference no: EM131137232
With reference to Exercise 78, use the result of part (b) of Exercise 39 to construct a 99% confidence interval for the mean weekly net profit of restaurants with a seating capacity of 210 at a location where the daily traffic count averages 14,000 cars.
Exercise 78
The following are data on the average weekly profits (in $1,000) of five restaurants, their seating capacities, and the average daily traffic (in thousands of cars) that passes their locations:
(a) Assuming that the regression is linear, estimate β0, β1, and β2.
(b) Use the results of part (a) to predict the average weekly net profit of a restaurant with a seating capacity of 210 at a location where the daily traffic count averages 14,000 cars
Exercise 39
If x01, x02, ... , x0k are given values of x1, x2, ... , xk and X0 is the column vector
it can be shown that
is a value of a random variable having the t distribution with n - k - 1 degrees of freedom.
(a) Show that for k = 1 this statistic is equivalent to the one of Exercise 23.
(b) Derive a (1 - α)100% confidence interval formula for
Exercise 23
Use the results of Exercises 20 and 21 and the fact that
Exercises 20
Under the assumptions of normal regression analysis, show that
(a) the least squares estimate of α in Theorem 2 can be written in the form
(b) 
has a normal distribution with
Theorem 2
Exercises 21
This question has been intentionally omitted for this edition.
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