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 s_e.

Weight (tons)	Cost ($ millions)
1.897	$ 53.6
3.019	184.8
0.453	6.4
0.975	23.5
1.058	32.6
2.100	110.4
2.379	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 = enter a number rounded to 4 decimal places  * + enter a number rounded to 4 decimal places * x
r² = enter a number rounded to 3 decimal places  **
s_e = enter a number rounded to 3 decimal places  **

Answer 1

	Weight (X)	Cost (Y)	X * Y	X2	Y2	Ŷ	(Y - Ŷ )2
	1.897	53.6	101.6792	3.5986	2872.96	86.9649	1113.2145
	3.019	184.8	557.9112	9.1144	34151.04	161.4872	543.4847
	0.453	6.4	2.8992	0.2052	40.96	-8.9445	235.4535
	0.975	23.5	22.9125	0.9506	552.25	25.7263	4.9566
	1.058	32.6	34.4908	1.1194	1062.76	31.2391	1.8519
	2.1	110.4	231.84	4.4100	12188.16	100.4480	99.0429
	2.379	104.6	248.8434	5.6596	10941.16	118.9789	206.7538
Total	11.881	515.9	1200.576	25.0578	61809.29	515.9000	2204.7579

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 7 * 1200.5763 - 11.881 * 515.9 ) / ( 7 * 25.057809 - ( 11.881 )²)
b = 66.4192

a =( ΣY - ( b * ΣX ) ) / n
a =( 515.9 - ( 66.4192 * 11.881 ) ) / 7
a = -39.0324
Equation of regression line becomes Ŷ = -39.0324 + 66.4192 X

r = 0.953

Coefficient of Determination
R² = r² = 0.907

Standard Error of Estimate S = √ ( Σ (Y - Ŷ ) / n - 2) = √(2204.7579 / 5) = 20.999