# Question: An aircraft company wanted to predict the number of worker hours

An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane’s top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company’s planes was taken, and the following model was estimated:

y = β0 + β1x1 + β2x2 + β3x3 + ε

where

y = design effort, in millions of worker-hours

x1 = plane’s top speed, in miles per hour

x2 = plane’s weight, in tons

x3 = percentage of parts in common with other models

The estimated regression coefficients were as follows:

b1 = 0.661 b2 = 0.065 b3 = -0.018

The total sum of squares and regression sum of squares were found to be as follows:

SST = 3.881 and SSR = 3.549

a. Test the null hypothesis:

H0: β1 = β2 = β3 = 0

b. Set out the analysis of variance table.

y = β0 + β1x1 + β2x2 + β3x3 + ε

where

y = design effort, in millions of worker-hours

x1 = plane’s top speed, in miles per hour

x2 = plane’s weight, in tons

x3 = percentage of parts in common with other models

The estimated regression coefficients were as follows:

b1 = 0.661 b2 = 0.065 b3 = -0.018

The total sum of squares and regression sum of squares were found to be as follows:

SST = 3.881 and SSR = 3.549

a. Test the null hypothesis:

H0: β1 = β2 = β3 = 0

b. Set out the analysis of variance table.

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