A) What Is the Equation of the Least-Squares
Line for Predicting

question 16

Essay

a) What is the equation of the least-squares
line for predicting tenacity using amino
b) Graph the least squares best fit line on the scatter plot
that appears on the next page.
acid ratio Amino acid ratio and tenacity for linings for 16 Japanese kimonos
$\begin{array}{|c|c|}\hline \begin{array}{c}\text { Amino acid } \\\text { ratio }\end{array} & \text { Tenacity } \\\hline 2.05 & 1.20 \\1.78 & 1.60 \\2.08 & 1.30 \\2.62 & 0.90 \\2.00 & 1.80 \\1.92 & 1.60 \\1.89 & 1.20 \\1.32 & 2.40 \\1.20 & 3.10 \\1.63 & 2.80 \\1.05 & 4.40 \\1.60 & 3.00 \\1.60 & 2.10 \\1.98 & 3.10 \\2.16 & 1.40 \\2.10 & 1.90 \\\hline\end{array}$
c) Approximately what proportion of the variability in
tenacity is explained by the linear relationship
between tenacity and the amino acid ratio? The theory of fiber strength suggests that the relationship between fiber tenacity and amino acid ratio is logarithmic, i.e. $\hat { T } = \alpha + \beta \log ( R )$ , where $T$ is the tenacity and $R$ is the amino acid ratio. Perform the appropriate transformation of variable(s) and fit this logarithmic model to the data. protein and biodegradable. It would be beneficial
to be able to assess the delicacy of a fabric before
making decisions about displaying it in a
museum. Chemical analysis might give some
evidence about the brittle nature of a fabric. Bio-
chemical data were acquired from the linings of
Some delicate fabrics are natural silks, made of sixteen 19th and early 20th century Japanese
kimonos. Investigators measured the
concentration of certain amino acids ("Amino
acid ratio") as well as the breaking stress
("tenacity") of the 16 kimono fabrics.

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Definitions:

Investment Turnover

A ratio that measures the efficiency of a company in using its investments to generate sales revenue.

Operating Expenses

Costs associated with the daily operations of a business, excluding direct costs of producing goods or services.

Cost Of Goods Sold

The direct costs attributable to the production of the goods sold by a company, including the cost of materials and labor.

Investment Turnover

A ratio that measures the efficiency of a company in using its investments to generate sales revenue, reflecting how effectively assets are being utilized.