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: x1 = Length of time an employee was in the industry x2 = Mechanical aptitude test score x3 = Prior on-the-job rating x4 = Age Performance on the new machine is designated y. Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are: Performance on New Machine, Length of Time in Industry, Mechanical Aptitude Score, Prior On-the-Job Performance, Age, Name y x1 x2 x3 x4 Mike Miraglia 118 11 343 122 50 Sue Trythall 116 8 307 128 21 The equation is: y ˆ   y⁢^⁢  = 10.2 + 0.2x1 + 0.486x2 + 0.812x3 + 0.008x4 What is this equation called? Multiple regression equation Multiple standard error of estimate Coefficient of determination How many dependent and independent variables are there? What is the number 0.486 called? Regression coefficient Coefficient of determination Homoscedasticity Multicollinearity 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 11 years and scored 220 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 95, and he is 57 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

The given equation is

^{^}=10.2+0.2x1+0.486x2+0.812x3+0.008x4.

Where is performance on the new machine,x1 is length of time was an employee in the industry, x2 is mechanical aptitude test score , x3 is Prior on the job rating and  x4 is age.

This equation is called multiple linear regression equation or multiple regression equation.

Only dependent variable here is and there are four independent variables. The four independent variables are x1,x2,x3,x4.

The value 0.486 is the regression coefficient of variable x2.

The regression coefficient in the case of multiple linear regression can be defined as the amount of change that occurs in the dependent variable when a unit change in the particular independent variable occurs, with all other independent variables are held constant. That is, in this case the independent variable x2 i.e. the mechanical aptitude test score. Then it can be explained as, there will be a 0.486 unit increase in the estimated performance of new machine, if the mechanical aptitude test score is increased by one unit.

The regression coefficient of age is 0.008. so as the age increases by 1 yr the estimated performance of the new machine will increase by 0.008 units.

Considering the details of Carl Knox

length of time was an employee in the industry x1 = 11yrs

Mechanical aptitude test score x2 =220

Prior on the job rating x3=95

and age x4= 57.

Applying this into the estimated regression formula, Carl's The performance on the new machine  is,

^{^}=10.2+0.2x1+0.486x2+0.812x3+0.008x4

^{^}=10.2+0.2*11+0.486*220+0.812*95+0.008*57

=196.916

That is Carl's estimated performance on the new machine is 196.916.