# Question

Flyer Computer, Inc., wishes to know the effect of various variables on labor efficiency. Based on a sample of 64 observations, the following model was estimated by least squares:

where

y` = index of direct labor efficiency in production plant

x1 = ratio of overtime hours to straight-time hours worked by all production workers

x2 = average number of hourly workers in the plant

x3 = percentage of employees involved in some quality-of-work-life program

x4 = number of grievances filed per 100 workers

x5 = disciplinary action rate

x6 = absenteeism rate for hourly workers

x7 = salaried workers’ attitudes, from low (dissatisfied) to high, as measured by questionnaire

x8 = percentage of hourly employees submitting at least one suggestion in a year to the plant’s suggestion program

Also obtained by least squares from these data was the fitted model:

y` = 9.062 - 10944x1 + 0.320x2 + 0.019x3 R2 = 0.242

The variables x4, x5, x6, x7, and x8 are measures of the performance of a plant’s industrial relations system.

Test, at the 1% level, the null hypothesis that they do not contribute to explaining direct labor efficiency, given that x1, x2, and x3 are also to be used.

where

y` = index of direct labor efficiency in production plant

x1 = ratio of overtime hours to straight-time hours worked by all production workers

x2 = average number of hourly workers in the plant

x3 = percentage of employees involved in some quality-of-work-life program

x4 = number of grievances filed per 100 workers

x5 = disciplinary action rate

x6 = absenteeism rate for hourly workers

x7 = salaried workers’ attitudes, from low (dissatisfied) to high, as measured by questionnaire

x8 = percentage of hourly employees submitting at least one suggestion in a year to the plant’s suggestion program

Also obtained by least squares from these data was the fitted model:

y` = 9.062 - 10944x1 + 0.320x2 + 0.019x3 R2 = 0.242

The variables x4, x5, x6, x7, and x8 are measures of the performance of a plant’s industrial relations system.

Test, at the 1% level, the null hypothesis that they do not contribute to explaining direct labor efficiency, given that x1, x2, and x3 are also to be used.

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