Question

A management consultant is studying the factors affecting the amount of time that it takes system administrators to complete tasks. In particular, she is interested in predicting the amount of time (in minutes) that it will take administrators to complete tasks, based on a set of variables collected for the engagement. The independent variables include – the age of the administrator (“Age”), the number of months of administrative job experience (“Experience”), whether or not the administrator has taken a job training (“Training”), and the level of complexity of the task as rated on a scale from 1 to 5 (“Complexity”). The dependent variable of interest is the amount of time (in minutes) that it takes the administrator to complete the assignment (“Performance”). Data are collected on the performance of 250 randomly selected administrators, each of whom was assigned a task to complete. The following regression model emerged using a training data, as a result of several rounds of modeling. Assume that all parameters appearing in the model are statistically significant at 0.05 level, that no multicollinearity was detected among the independent variables, and that the residual diagnostics did not show serious violations of underlying assumptions. In addition, assume that complexity grows in a linear fashion. Note, that in the validation set the variables that do not show up in the final regression equation are omitted

E.V.(Performance) = 55 - 0.2 x Experience + 15 x Complexity

Question 1. By how many minutes is the performance time estimated to change on average when experience goes up by 10 months, all else kept constant? Does it go up or down?(in X minutes)

Question 2. By how many minutes does the performance time change on average when complexity goes up by 1, all else kept constant? Does it go up or down? (in X minutes)

Answer 1

Given to us is the linear model as below:

E.V.(Performance) = 55 - 0.2 x Experience + 15 x Complexity

General theory regarding interpretation of regression coefficient: let there be model : E( y)= a +bx +cz , where b and c are regression coefficients then we interpret b as the change in expected value of y when there is unit change in x keeping other things constant. Similarly c can be interpreted as the change in expected value of y when there in unit change in z.

Mathematically it can be written as and similarly      .  

Using this in our model we follow as below:

Question1:  

It goes down by 2 minutes

Question 2:

Thus with change in complexity by 1 the time take goes up by 15 minutes