Example 1. Simple Linear Regression: Service Calls Data

A company which markets and repairs small computers needs to forecast the number of service engineers required over the next few years. This requires consideration of the length of service calls, which in turn depends on the number of components that need to be repaired or replaced. The data given in Table 1 consists of the number of components repaired and the length of the service call (in minutes) for a random sample of 20 calls. We will use a simple regression model to explain the relationship between the length of service call (response variable) and the number of repaired units (predictor variable).

Source:Chatterjee, S. and Price, B. (1991). Regression Analysis by Example. John Wiley & Sons: New York.

Table 1: Number of repaired components and time (length) of service (in minutes)

No.    Time      No.     Time
1       23       10      154
2       29       10      166
3       49       11      162
4       64       11      174
4       74       12      180
5       87       12      176
6       96       14      179
6       97       16      193
7      109       17      193
8      119       18      195
9      149       18      198
9      145       20      205

Questions:

1. Assess whether there is a relationship between the number of units X, and service time in minutes Y using graphical and numerical techniques.
   
   
2. Fit a simple linear regression model relating service time (response) to units repaired (predictor), making required assumptions. Discuss verification of these assumptions.
   
   
3. Construct suitable residual analysis.
   
   
4. Assess overall goodness of fit of the regression line.
   
   
5. Discuss the use of this model for prediction.

Keywords: Scatter plot, correlation, least squares, normal distribution, t-test, F-test, residuals