Question

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 1995 to 2005 (inclusive), the following model was estimated: Y = -6.46 + 1.68 X

                 Error sum of squares: 324.8        Sum of squares of X: 986.9

Determine the upper limit for the 95% confidence interval for the slope correct to two decimal places.

Answer 1

From the equation, estimate of slope , $\hat \beta_1$ = 1.68

Here number of observations, n = 11

$\alpha$ = 0.05

degrees of freedom, df = n-2 = 9

So, $t_{\alpha/2, df} = t_{0.025, 9} = 2.262$ (From t-table: two tailed test)

Standard error of slope estimate,

$se(\hat \beta_1) = \sqrt{\frac{SSE/(n-2)}{S_{xx}}} = \sqrt{\frac{324.8/9}{986.9}} = 0.19122$

So, upper limit of the confidence interval,

$= \hat \beta_1 + t_{0.025, 9} * se(\hat \beta_1) = 1.68 + 2.262 * 0.19122 = 2.11$ (Ans)

** If the answer does not match please comment.