Question

Assume you discovered from historical records that simple linear regression is an effective means of predicting the labor cost of some project tasks. You found that the weight associated with an item (in pounds) produced in historical projects is an accurate and reliable predictor of labor cost. You develop a linear equation expressing the relationship between item weight and labor cost: estimated demand = 1,300 + 0.25x For an upcoming project that includes the task of manufacturing an item weighing 7,000 pounds, estimate the task cost using this regression equation.

a. $1,750

b. $3,000

c. $3,050

d. None of the above are correct.

Answer 1

The labor cost of manufacturing an item that weighs 7,000 pounds using the given regression equation is $3,050, which corresponds to option (c).

Step-by-step explanation:

To estimate the task cost using the provided simple linear regression equation:

estimated labor cost = 1,300 + 0.25x,

where x represents the weight of the item in pounds, we need to substitute x with the weight of the item for the upcoming project, which is 7,000 pounds.

estimated labor cost = 1,300 + 0.25(7,000)

estimated labor cost = 1,300 + 0.25 × 7,000

estimated labor cost = 1,300 + 1,750

estimated labor cost = 3,050

Therefore, the estimated labor cost of manufacturing an item that weighs 7,000 pounds is $3,050, which corresponds to option (c).

To estimate the labor cost, the item weight is plugged into the linear regression equation which predicts labor cost based on the weight. After calculation, the estimated labor cost for a 7,000-pound item is $3,050.