Performance on the new machine

Question

Q1. Thompson Photo 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. (LOTM)
X₂ = Machanical aptitude test score. (MAS)
X₃ = Prior on-the-job rating. (OTJT)
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 recorder. A few results are:

Name         Performance     LOTM     MAS    OTJP     Age
Andy Kosin      112              12        312     121       52
Sue Annis       113               2         380     123       27

The equation is:

Y1 (upper) = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4

a. What is the equation called?

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 machines increase?

e. Carl Knox applied for the job at Photo Works. He has been a machinist for six years, and scored 280 on the MAS. Carl's prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl's performance on the new machine.

Q2. Cellulon, a manufacturer of a new type of home insulation, wants to develop guidelines for builders and consumers regarding the effects on natural gas consumption (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature. In the laboratory they varied the insulation thickness and temperature. A few of the findings are:

Mo. Nat. Gas     Thickness of        Outdoor
Consumption      Insulation         Temperature
(cubic ft)             (cm)               (Celsius)

    Y                     X1                   X2
30.3                   12.5                    4
26.9                    30                      4
22.1                    20                      9

Based on the sample results, the regression equation is:

Y₁ (upper) = 38.12 - 0.194X₁ - 1.349X₂

a. How much natural gas can homeowners expect to use per month if they install 15cm of insulation and the outdoor temperature is 10 degrees Celsius.

b. What effect would installing 18cm of insulation instead of 15 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 10 degrees Celsius)?

c. Why are the regression coefficients, b1 and b2, negative? Is this logical?