For the following data calculate the correlation coefficient and plot the data on a scatter diagram. Do you think it measures the strength of the relationship accurately?

x 1 2 3 4 5 6 7 y 8.25 7 6.25 6 6.25 7 8.25 2 Return to the variables used in Chapter 9, Exercise 3. In that exercise you were required to obtain a trend for each variable using moving averages. For each trend that you obtained, forecast the trend one year into the future using regression.

Evaluate the result both statistically and in the context of the variable. Assess how reliable you think such a forecast would be for each variable.

The next stage was to try to quantify some of these key relationships and then try to develop predictions of key performance variables based on assumed changes in key influences. It was decided to adopt a regression-modelling approach to this analysis. At an operational level the RAC divides the UK into six regions, with each region further split into zones (denoted by a letter). One particular region, Central England, was used to assess whether the modelling approach was feasible and data collected on the 17 zones of this region

(denoted as zones A to Q). As is usual with this approach, the data collection process itself was no easy task. Because of previous organisational changes a few years earlier, it was felt appropriate to collect data only for the period after this change

(limiting the amount of data that could be used for modelling). The geographical boundaries of some zones had also altered. Some data was available internally from the CARS system, while other data had to be collected externally (weather information, pollution statistics). The influence map was used to identify the key dependent variables of interest and then the potential independent variables influencing each dependent variable. The multiple regression approach that has been described in this chapter was adopted to try to develop appropriate multiple regression models. Scatter plots were used to assess initial linearity (or non-linearity in some cases). R
2 values were assessed, as were residuals, which were examined to test the basic multiple regression assumptions. An iterative approach was adopted until acceptable regression equations had been obtained. A total of 12 equations were developed in this way, with the format of each illustrated in Figure 10.23 (note that for reasons of commercial confidentiality the numerical parameters of the equations are not reported). So, for example, the Customer Satisfaction Index was found to be dependent on five key variables: OLOS (the overall level of service), ROLOS (the recovery overall level of service), VFR (the vehicle fix rate), Jobs
Service breakdown and Rescue PAR.

Further analysis of these equations led to five of the estimated equations being used for what-if modelling purposes, with output from the model equations shown for one zone in Figure 10.24. The authors of the article comment that ‘this modelling methodology ... [stimulated a] new understanding of the business environment’, with management now intending to develop a national model using the same fundamental approach.

392 10 FORCASTING II: REGRESSION This application is based on the article ‘Corporate Modelling at RAC Motoring Services’, S Clarke, A Hopper, A Tobias and D Tomlin, Operational Research Insight 9 (3), 1996, pp 6
–
12.

The figures in this section are reproduced with permission of the Operational Research Society.