To ensure that as many trial subscriptions as possible are converted to regular subscriptions, the Herald marketing department works closely with the distribution department to accomplish a smooth initial delivery process for the trial subscription customers. To assist in this effort, the marketing department needs to accurately forecast the number of new regular subscriptions for the coming months. A team consisting of managers from the marketing and distribution departments was convened to develop a better method of forecasting new subscriptions. Previously, after examining new subscription data for the prior three months, a group of three managers would develop a subjective forecast of the number of new subscriptions. Lauren Hall, who was recently hired by the company to provide expertise in quantitative forecasting methods, suggested that the department look for factors that might help in predicting new subscriptions. Members of the team found that the forecasts in the past had been particularly inaccurate because in some months, much more time was spent on telemarketing than in other months. In particular, in the past month, only 1,055 hours were completed because callers were busy during the first week of the month attending training sessions on the personal but formal greeting style and a new standard presentation guide. Lauren collected data for the number of new subscriptions and hours spent on telemarketing for each month for the past two years.
a. Analyze the data and develop a regression model to predict the number of new subscriptions for a month, based on the number of hours spent on telemarketing for new subscriptions.
b. If you expect to spend 1,200 hours on telemarketing per month, estimate the mean number of new subscriptions for the month. Indicate the assumptions on which this prediction is based. Do you think these assumptions are valid? Explain.
c. What would be the danger of predicting the number of new subscriptions for a month in which 2,000 hours were spent on telemarketing?