Question

1. The Maroochy Chamber of Commerce is interested in determining the relationship between the number of fine days each year and the number of interstate and overseas tourists visiting the Sunshine Coast each year, measured in thousands. Using annual data from 1993 to 2005 (inclusive), the following model was estimated: Y = -4.13 + 0.66 X

   
                    Error sum of squares: 354.7        Sum of squares of X: 915.2

   
   Determine the upper limit for the 90% confidence interval for the slope correct to two decimal places.

Answer 1

SOLUTION:

Y = -4.13 + 0.66 X

Slope coefficient = 0.66 ; n = 13 (1993 - 2005) inclusive

Std Error = sqrt [Error sum of squares / (n-2) ] / sqrt ( Sum of squares of X)

               = sqrt[354.7/(13 - 2)] / sqrt[915.2] = 0.1877

alpha = 1 - 0.90 = 0.10

Degrees of freedom = n - 2 = 11

Critical value for alpha = 0.10 and df = 11 is +1.795

Margin of error = critical value * Std error = +1.795 * 0.1877 = +0.33

upper limit for the 90% confidence interval for the slope = Slope coefficient + Margin of error

                                    = 0.66 + 0.33 = 0.99   1.