Question

A clothing manufacturer wants to estimate the amount of scrap cloth generated each day by its fabric cutting machines. Eight potential independent variables have been identified, including, for example,

=x1 amount of cloth run through cutting machines (in square feet),

=x2 machine cutting speed (in feet per minute),

=x8 age of machine (in years).

The manufacturer selects 7 of the candidate independent variables to use in a multiple regression model for estimating y, the amount of scrap cloth (in square feet). Using data collected from 20 different cutting machines operating on different days, the model =y+β0+β1x1+β2x2+...β7x7 is fit to the data. Fill in the blanks in the analysis of variance (ANOVA) table associated with this model. Do all calculations to at least three decimal places.

Source of Variation Degrees of Freedom Sums of Squares Mean Squares F Statistic Regression 58 Error 40 Total

Answer 1

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Squares	F Statistic
Regression	7	406	58	17.4000
Error	12	40	3.3333
Total	19	446

>> Calculations:

sample size , n = 20 Number of independent variables, k=7 degrees of freedom for Regreexion = K = 7 degrees of freedom for Total = n-1 = 20-1 = 19 degrees of freedom for Enor = n-K-1 = 20-7-1 = 12 Sum of squares for Regression = 58 * 7 = 406 Sum of squares for Error = 40 Sum of squares for Total = 406+40 = 446 Mean squares for Regrenion = 58 Mean Squares for Error = 40 = 3.3333 F statistie = 58cm = 17.4000