In Simple Linear Regression, Most Often We Perform a Two-Tail $$\beta _ { 1 }$$

question 100

Short Answer

In simple linear regression, most often we perform a two-tail test of the population slope $$\beta _ { 1 }$$ to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance? $\begin{array}{|l|l|}\hline A&H_{0}: \beta_{0}=0 \\&\mathrm{H}_{\mathrm{a}}: \beta_{0} \neq 0\\\hline B&\mathrm{H}_{0}: \beta_{1} \neq 0\\&\mathrm{H}_{a}: \beta_{1}=0 \\\hline C&\mathrm{H}_{0}: \beta_{0}=0 \\&\mathrm{H}_{\mathrm{a}}: \beta_{0} \neq 0\\\hline D&\mathrm{Ho}: \beta_{1}=0\\&\mathrm{H}_{a}: \beta_{1} \neq 0 \\\hline \end{array}$

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Definitions:

Dilute Acid

An acid solution that has a low concentration of acid in a large amount of solvent, typically water.

Malonic Ester

A compound characterized by having two ester groups attached to the same carbon, which is notable for its use in malonic ester synthesis, allowing the construction of carboxylic acids.

Major Organic Product

The primary product of a chemical reaction involving organic compounds, typically the one produced in the greatest yield.

Stepwise Mechanism

A reaction mechanism that occurs in multiple discrete stages, with each step having its own transition state and intermediates.