A firm has modeled its experience with industrial accidents and found that the number of accidents per year (y-hat) is related to the number of employees (x) by the regression equation:
y-hat = 3.3 + 0.049x. The r-squared value is 0.68.
The regression is based on 20 annual observations. The firm intends to employ 480 workers next year. How many accidents do you project? How much confidence do you have in that forecast?
y-hat = 3.3 + 0.049(480 ) = 3.3 + 23.52 = 26.82 accidents. This is not a time series, so next year = year 21 is of no relevance. Confidence comes from the coefficient of determination; the model explains 68% of the variation in number of accidents, which seems respectable.
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