Thompson Photo Works purchased several new, highly sophisticated processing mach

Question

Thompson Photo Works purchased several new, highly sophisticated processing 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 an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed:

  

  

  

      Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are:

  

  

  

  

  

  

  

As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.)

  

Carl Knox applied for a job at Photo Works. He has been in the business for 3 years and scored 360 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 70, and he is 63 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

X1 = Length of time an employee was in the industry X2 = Mechanical aptitude test score X3 = Prior on-the-job rating X4 = Age

Explanation / Answer

a. This is a question from an area of statistics called correlation and regression.

The idea is that you can estimate an dependent variable Y, as a function of a number of independent variables X, with various weightings assigned to each X variable.

This equation is therefore called a regression equation

b) There is only 1 dependent variable, namely Y and four independent variables, namely X1, X2, X3 and X4. You can see this by noting that if you take another employee, all four X's will change, since they are all properties (qualities) of the individual. But if you know all 4 of these properties, you will be able to calculate Y, so Y depends on X1, X2, X3 and X4.
c. Critical value
d) Age increasing by one year means adding 1 to X4. So if you call Ya the performance on the machine by a employee A with age X4a and the other variables just X1, X2 and X3 then:
Ya = 11.6 + .4*X1 + .286*X2 + .112*X3 + .002*X4a
Now if we take another employee, B, with all the same qualities as employee A except that employee B is one year older. Then all the qualities X1, X2 and X3 are both the same for A and B. However: X4b = X4a +1 since B is one year older.
Now: Yb= 11.6 + .4*X1 + .286*X2 + .112*X3 + .002*X4b = 11.6 + .4*X1 + .286*X2 + .112*X3 + .002*(X4a + 1) = 11.6 + .4*X1 + .286*X2 + .112*X3 + .002*X4a + .002 = Ya +.002 (remember that Ya = 11.6 + .4*X1 + .286*X2 + .112*X3 + .002*X4a) So by increasing age by one year, Y increases by 0.002.

e) Here we are apparently given all the values for X1 to X4. So if we insert these values in the expression for Y we get:

Y = 11.6 + 0.4*6 + 0.286*280 + 0.112*97 + 0.002*35 = 105.014

Thus we estimate Carl's performance to be 105.014.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.