Question

"The director of special events for Sun City believed that the amount of money spent on fireworks displays for the Fourth of July was predictive of attendance at the Fall Festival held in October. She gathered the following data to test her suspicion.

4th of July ($000) Fall Festival (000) 4th of July ($000) Fall Festival (000)
8.0 6.8 12.0 9.5
6.0 6.4 7.5 10.4
12.0 11.6 9.0 6.6
10.5 10.2 10.6 10.1
8.5 6.0 10.0 6.1
12.5 11.1 7.5 9.0
9.0 7.5 10.0 12.6
5.5 8.4
a-1. Compute and report the regression equation that predicts "fall festival attendance" with "amount spent on Fourth of July fireworks". (Round your answers to 2 decimal places.)
a-2. Report the coefficient of determination. (Round your answer to 2 decimal places.) %
a-3. Interpret the regression coefficient. (Round your answer to 4 decimal places.)
b. Evaluate the regression assumptions based on an analysis of the residuals .
The regression assumptions based on an analysis of the residuals is_______.

Answer 1

ŷ = 0.52X + 3.99 ;

0.26 ;

0.5123

Explanation:

4th of July :

8.0

6.0

12.0

10.5

8.5

12.5

9.0

5.5

12.0

7.5

9.0

10.6

10.0

7.5

10.0

Fall festival :

6.8

6.4

11.6

10.2

6.0

11.1

7.5

8.4

9.5

10.4

6.6

10.1

6.1

9.0

12.6

Using technology, the regression equation which predicts fall festival attendance with amount spent on 4th of July fireworks is ;

ŷ = 0.52X + 3.99

Coefficient of determination ; R² is 0.26

This means that about 26% of variation in the fall festival attendance is explained by the regression line.

The regression Coefficient, R = sqrt(R²) = sqrt(0.2625) = 0.5123

This depicts that a faiy strong positive correlation exists between the amount spent on 4th July fireworks and the fall festival attendance.