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	184.5
0.453	6.4
0.987	23.5
1.058	33.5
2.100	110.4
2.408	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

The excel regression output for this problem is:

Simple linear regression results: Dependent Variable: Cost (5 millions) Independent Variable: Weight (tons) Cost (millions) = -35.633482 +67.501336 Weight (tons) Sample size: 6 R (correlation coefficient) = 0.97871792 R-sq=0.95788877 Estimate of error standard deviation: 15.619009 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -35.633482 13.433579 0 4 -2.652568 0.0568 Slope 67.501336 7.0765859 0 4 9.5386868 0.0007

Hence,

$\widehat{y}$= -35.6335 + 67.5013 x

r2 = 0.958

se = 15.619