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Working with operators

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If |0> and |1> denote the two eigenstates of N corresponding to the eigenvalues 0 and 1, respectively, show that

câ?  |0> = |1> and c |0> = 0

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Regression problem

Thompson Machine Works purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as a machine operator important? In order to explore further the factors needed to estimate performance on the new machines, four variables were listed:
X1 _ Length of time employee was a machinist. X3 _ Prior on-the-job rating.
X2 _ Mechanical aptitude test score. X4 _ Age.
Performance on the new machine is designated Y.Thirty machinists were selected at
random. Data were collected for each, and their performances on the new machines
were recorded. A few results are listed in the attached file.

The equation is: Y _ 11.6 _ 0.4X1 _ 0.286X2 _ 0.112X3 _ 0.002X4
a. What is the full designation of the equation?
b. How many dependent variables are there? Independent variables?
c. What is the number 0.286 called?
d. As age increases by one year, how much does estimated performance on the new machine increase?
e. Carl Knox applied for a job on a new machine. He has been a machinist for six years, and scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl's performance on the new machine.

See attached file for full problem description.

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