Question

The following table shows the number of customer complaints against airlines operating in a country during the given year.

Year	2002	2004	2006	2008	2010
Number of complaints	9472	7448	8313	10,640	16,494

Use interpolation to estimate the number of complaints in 2005.

(Round your answer to the nearest whole number.)

The interpolated value for

2005 is _______ complaints.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:

Dependent Variable: Number of Complaints
Independent Variable: Year
Number of Complaints = -1718297.4 + 861.8 Year
Sample size: 5
R (correlation coefficient) = 0.76248653
R-sq = 0.58138571
Estimate of error standard deviation: 2670.2425

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-1718297.4	846938.89	≠ 0	3	-2.0288328	0.1355
Slope	861.8	422.20242	≠ 0	3	2.041201	0.1339

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	29707970	29707970	4.1665016	0.1339
Error	3	21390586	7130195.2
Total	4	51098555

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
2005	9611.6	1266.6072	(5580.6904, 13642.51)	(206.14437, 19017.056)

Hence,

Predicted value for 2005 = 9612 complaints