Question

QUESTION 3

Suppose a study is conducted to find out how the cost of flying between Brisbane and Sydney using Boeing 737 varies with the number of passengers. The table below presents the number of passengers and associated costs for a random sample of 15 flights between Brisbane and Sydney using Boeing 737.

Number of passengers	71	63	66	68	48	73	50	81	50	92	56	80	55	67	84
Cost ($)	4480	4020	4420	4150	3800	4300	4090	4700	4000	5200	4650	4480	3980	4390	4880

Use the EXCEL regression output below to answer the questions that follow:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.83
R Square	0.70
Adjusted R Square	0.67
Standard Error	217.80
Observations	15.00
ANOVA
	df	SS	MS	F	Significance F
Regression	1.00	1414815	1414815	29.83	0.00
Residual	13.00	616677	47436
Total	14.00	2031493
	Coefficients	Standard Error	t Stat	P-value
Intercept	2793.64	293.95	9.50	0.00
Number of passengers	23.54	4.31	5.46	0.00

1. State and comment on the correlation between cost and passenger number.

2. State the regression equation and interpret the values of its intercept coefficient and slope coefficient.

3. State and interpret the coefficient of determination of the model.

4. Predict the cost of flying between Brisbane and Sydney given the number of passengers is 72.

Answer 1

i:

The correlation between cost and passenger number is 0.83. It is positive because slope is positive.

It shows a strong, linear and positive relationship between the variables.

ii:

The regression equation is

cost = 2793.64 + 23.54 * Number_of_passengers

Intercept: When number of passengers is zero cost of the flight is 2793.64.

Slope: For each additional customer, cost of the flight is increased by $23.54.

iii:

The coefficient of determination is 0.70.

It shows that 70% of variation in cost of flight is explained by number of customers.

iv:

cost = 2793.64 + 23.54 * Number_of_passengers = 2793.64 + 23.54 * 72 = 4488.52

Answer: $4488.52