Question

Running a manufacturing operation efficiently requires knowledge of the time it takes employees to manufacture the product, otherwise the cost of making the product cannot be determined. Estimates of production time are frequently obtained using time studies. The data in the table below came from a recent time study of a sample of 15 employees performing a particular task on an automobile assembly line.

Time to Assemble, y (minutes)	Months of Experience, x
10	24
20	1
15	10
11	15
11	17
19	3
11	20
13	9
17	3
18	1
16	7
16	9
17	7
18	5
10	20

1. Run the multiple linear regression model in SPSS. State the least squares prediction equation.
2. Test the null hypothesis H₀: β₂ = 0 against the alternative H_a: β₂ ≠0. Use α = .01. Does the quadratic term make an important contribution to the model?
3. Your conclusion in part b should have been to drop the quadratic term from the model. Do so and fit the “reduced model” y = β₀ + β₁x + ϵ to the data.
4. Define β₁ in the context of this exercise. Find a 90% confidence interval for β₁ in the reduced model of part c.                     

Answer 1

a)

Model 1

Regression Equation

Time to Assemble, y (minutes) = 20.09 – 0.67 * Experience + 0.01 * Expereience²

b)

Since the p-value for β₂ is greater than 0.01, we fail to reject the null hypothesis. ie the squared term is not significant in the model.

c)

Model 2

Regression Equation

Time to Assemble, y (minutes) = 19.28 – 0.44 * Experience

d)

Interpretation of Slope:

The amount by which the response variable (Time to Assemble) increases or decreases, on average, when the explanatory variable (Experience) increases by one.

90% CI for Slope = -0.44 +/- 1.64 * 0.04 = {-0.51, -0.38}