The Following Data Show the Results of an Aptitude Test

question 27

Essay

The following data show the results of an aptitude test Y) and the grade point average of 10 students.
$\begin{array}{ll}\text { Aptitude Test }\\\text { Score Y) }&\text { GPA X) }\\26 & 1.8 \\31 & 2.3 \\28 & 2.6 \\30 & 2.4 \\34 & 2.8 \\38 & 3.0 \\41 & 3.4 \\44 & 3.2 \\40 & 3.6 \\43 & 3.8\end{array}$
a. Develop a least squares estimated regression line.
b. Compute the coefficient of determination and comment on the strength of the regression relationship.
c. Is the slope significant? Use a t test and let α = 0.05.
d. At 95% confidence, test to determine if the model is significant i.e., perform an F test).

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Definitions:

PhOH

Phenol, an aromatic compound with the formula C6H5OH, known for its antiseptic properties.

Reactive Intermediate

A reactive intermediate is a short-lived, high-energy molecule formed during the conversion of reactants into products in a chemical reaction.

Addition Polymers

Polymers formed by the sequential addition of monomers without the loss of any molecule.

Step-growth

A polymerization process where chains grow by the stepwise reaction between functional groups, leading to high molecular weight polymers.