Question

People in the aerospace industry believe the cost of a space project is a function of the mass of the major object being sent into space. Use the following data to develop a regression model to predict the cost of a space project by the mass of the space object. Determine r2 and se.

Weight (tons)	Cost ($ millions)
1.897	$ 53.6
3.019	185.0
0.453	6.4
0.980	23.5
1.058	34.1
2.100	110.4
2.377	104.6

*(Do not round the intermediate values. Round your answers to 4 decimal places.)
**(Round the intermediate values to 4 decimal places. Round your answer to 3 decimal places.)


ŷ = ( ) * + ( ) * x
r2 = ( ) **
se = ( ) **

Please Fill in the ( ) blanks

Thanks

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Cost ($ millions)
Independent Variable: Weight (tons)
Cost ($ millions) = -35.788407 + 67.961394 Weight (tons)
Sample size: 6
R (correlation coefficient) = 0.98063441
R-sq = 0.96164384
Estimate of error standard deviation: 14.924177

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-35.788407	12.834427	≠ 0	4	-2.7884694	0.0494
Slope	67.961394	6.7864506	≠ 0	4	10.014277	0.0006

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	22336.749	22336.749	100.28574	0.0006
Error	4	890.92426	222.73107
Total	5	23227.673

Hence,

ŷ = -35.7884 + 67.9614 x

r2 = 0.962

se = 14.924