(b) What fraction of the raw variability in the strength of wood beams is accoun
ID: 3051510 • Letter: #
Question
(b) What fraction of the raw variability in the strength of wood beams is accounted for by the two equations?
For Question 1:
For Question 2:
Please show work for all, I want to compare my answers. Thanks
The data used in creating the attached JMP output (see separate sheet) are collected in order to study the effects of two independent vanables x1-spec e gravity and r2 = moisture content on the response variable y = strength of wood beams. Answer the following questions from the output: (a) What were the two least square equations fit to the data? Equation 1: y= Equation 2: y (b) What fraction of theraw variability in the strength of wood beams is accounted for by the two equations? For equation 1: For equation 2:Explanation / Answer
a) The two least square equations from the given data are
Y = 18.043 - 0.6242 x2
Y = 10.279 + 8.6435 x1 - 0.2723 x2
The estimates are the coefficients of the corresponding terms.
b) The fraction of the raw variability in the strength of wood beams accounted by the two equations is nothing but R2.
For equation 1 R2 = 0.5764 and so 57.64% of variance in the dependent variable is explained by the independent variable.
For equation 2 R2 = 0.9031 and so 90.31% of variance in the dependent variable is explained by the independent variable.
By looking at the values second equation explains more variance in the dependent variable.
R2 is also called as coefficient of determination. The higher the value the reliable the equation. It is measure of variance explained.
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