Acommon mathematical interpretation of of causal relations is y =f(x,ε), where f is the law of nature and ε is some random noise. having observed data that is likely generated the equation, there are two goals in the data analysis: (1) extracting information about the law of nature—the function f (where we are mostly care about in chemical engineering). (2) predict what the response variables y are going to be with the predictor variables x revealed to us.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?