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) 1.897, 3.019, 0.453, 0.979, 1.058, 2.100, 2.408, Cost ($ millions) 53.6, 184.7, 6.4, 23.5, 33.4, 110.4, 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 =?**

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1.897	53.6	0.04	408.04	-3.94
3.019	184.7	1.73	12298.81	146.06
0.453	6.4	1.56	4542.76	84.18
0.979	23.5	0.52	2530.09	36.37
1.058	33.4	0.41	1632.16	26.02
2.1	110.4	0.16	1339.56	14.57
2.408	104.6	0.50	948.64000	21.7448

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	11.91	516.60	4.93	23700.06	325.00
mean	1.70	73.80	SSxx	SSyy	SSxy

sample size ,   n =   7          
here, x̅ = Σx / n=   1.702   ,     ȳ = Σy/n =   73.800  
                  
SSxx =    Σ(x-x̅)² =    4.9268          
SSxy=   Σ(x-x̅)(y-ȳ) =   325.0          
                  
estimated slope , ß1 = SSxy/SSxx =   325.0   /   4.927   =   65.96446
                  
intercept,   ß0 = y̅-ß1* x̄ =   -38.47150          
                  
so, regression line is   Ŷ =   -38.472   +   65.964   *x
R² =    (Sxy)²/(Sx.Sy) =    0.905
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    2261.9417
      
std error ,Se =    √(SSE/(n-2)) =    21.269