The Norwegian architecture company, Invent as Design, wants to predict the number of worker-hours necessary  to finish the design of a new building in Tromsø. Relevant explanatory variables were thought to be the number of floors in the building, the weight of materials, and the number of parts it had in common with other structures built by the company. A sample of 23 of the company’s structures was taken, and the following model was estimated: 

where
y = design effort, in millions of worker-hours
x₁ = number of floors in the building
x₂ = the weight of materials, in tons
x₃ = percentage of parts in common with other buildings
The estimated regression coefficients were as follows:
b₁ = 0.631, b₂ = 0.066, b₃ = 0.017
The estimated standard errors were as follows:
sb₁ = 0.096, sb₂ = 0.037, sb₃ = 0.0023
a. Find 90% and 95% confidence intervals for β₁.
b. Find 95% and 99% confidence intervals for β₂.
c. Test against a two-sided alternative the null hypothesis that, all else being equal, the plane’s weight has no linear influence on its design effort.
d. The error sum of squares for this regression was 0.397. Using the same data, a simple linear regression of design effort on the percentage of common parts was fitted, yielding an error sum of squares of 3.397. Test, at the 2% level, the null hypothesis that, taken together, the variable’s number of floors and weight of materials contribute nothing in a linear sense to explaining the changes in the variable, design effort, given that the variable percentage of common parts is also used as an explanatory variable.

Transcribed Image Text:

y Bo B1x1 + B₂x2 + B3X3 + & =