1. The Maroochy Chamber of Commerce is interested in determining the relationshi

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 = -6.36 + 0.38 X
                 Error sum of squares: 303.6        Sum of squares of X: 976.2
Determine the upper limit for the 90% confidence interval for the slope correct to two decimal places.________

2.

The ANOVA table above is from a simple linear regression analysis relating the percentage alcohol content in diferent brands of beer to the number of kilojoules per 100mL. Determine the coefficient of determination as a percentage, correct to two decimal places. ___________

3. ANOVA

df

SS

Regression

1

0.72

Residual

10

62.6

Total

11

63.32

Coefficients

Std Error

Intercept

14.64

146.76

No. of accounts (000)

1.99

5.87

This printout is for data relating the number of ATM withdrawals (in thousands) to the number of accounts (in thousands) at that branch. Predict the number of withdrawals if the number of accounts is 24.528 thousand. State the answer in thousands correct to two decimal places.______________   

Explanation / Answer

1) Y = -6.36 + 0.38 X

Slope coefficient = 0.38 ; n = 13 (1993 - 2005) inclusive

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

               = sqrt[303.6/(13 - 2)] / sqrt[976.2] = 0.168

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 * 0.168 = +0.30

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

                                    = 0.38 + 0.30 = 0.68

2) coefficient of determination R2 = 1 - Residual SS / Total SS

                                                        = (1 - 63.64/275.78) * 100

                                                        = 76.92%

3) number of ATM withdrawals = 14.64 + 1.99 (number of accounts)

For number of accounts = 24.528 thousand

number of ATM withdrawals = 14.64 + 1.99 (24.528)

                                               = 63.45 thousand

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