A Quadratic Regression Model Is Fit to a Set of Sample

question 55

Multiple Choice

A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 29.73 and that the y-values are 11, 14, 19, 22, 26, 27,
Find $$R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } } \text {. }$$

• A) \(0.844\)
• B) \(0.144\)
• C) \(0.88\)
• D) \(0.856\)

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Definitions:

Degrees of Freedom

The number of independent values or quantities that can be assigned to a statistical distribution or to a system of equations, minus the number of equations constraining them, crucial in significance testing.

Completely Randomized Design

A type of experimental design where all subjects are randomly assigned to treatments without any restrictions or stratifications.

Test Statistic

A value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis.

Mean Square

A method used in statistical analysis that takes the sum of squares of variables divided by their degrees of freedom, often used in the context of ANOVA.