Question

Listed below are altitudes​ (thousands of​ feet) and outside air temperatures​ (°F) recorded during a flight. Find the​ (a) explained​ variation, (b) unexplained​ variation, and​ (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear​ correlation, so it is reasonable to use the regression equation when making predictions. For the prediction​ interval, use a​ 95% confidence level with the altitude of 6327 ft​ (or 6.327 thousand​ feet).

Altitude Temperature

2	55
9	33
16	23
21	0
27	-26
31	-41
34	-50

a. Find the explained variation.

b. Find the unexplained variation.

c. Find the indicated prediction interval.  

Answer 1

The statistical software output for this problem is :

Simple linear regression results:
Dependent Variable: Temp
Independent Variable: Altitude
Temp = 66.244306 - 3.3550725 Altitude
Sample size: 7
R (correlation coefficient) = -0.99077002
R-sq = 0.98162523
Estimate of error standard deviation: 5.9070439

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	66.244306	4.673472	≠ 0	5	14.174538	<0.0001
Slope	-3.3550725	0.20528397	≠ 0	5	-16.343568	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	9320.3913	9320.3913	267.11221	<0.0001
Error	5	174.46584	34.893168
Total	6	9494.8571

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
6.327	45.016763	3.5865209	(35.797318, 54.236208)	(27.252518, 62.781007)

(a) explained variation = R-sq = 0.9816 = 98.16 %

(b) unexplained variation = 1-0.9816 = 0.0184 = 1.84%

(c) (27.252518, 62.781007)