A Regression Was Performed on a Sample of 20 Observations

question 37

Essay

A regression was performed on a sample of 20 observations. Two independent variables were included in the analysis, x and z. The relationship between x and z is z = x². The following estimated equation was obtained. = 23.72 + 12.61x + 0.798z
The standard errors for the coefficients are S_b1 = 4.85 and S_b2 = 0.21
For this model, SSR = 520.2 and SSE = 340.6
a.Estimate the value of y when x = 5.
b.Compute the appropriate t ratios.
c.Test for the significance of the coefficients at the 5% level. Which variable(s) is (are) significant?
d.Compute the coefficient of determination and the adjusted coefficient of determination. Interpret the meaning of the coefficient of determination.
e.Test the significance of the relationship among the variables at the 5% level of significance.

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Definitions:

Compound

A substance composed of two or more elements chemically combined in a fixed proportion, possessing unique properties differing from those of the constituent elements.

IUPAC Name

The systematic and standardized name given to a chemical substance based on the rules established by the International Union of Pure and Applied Chemistry.

Cyclic Amides

Compounds characterized by a ring structure in which one or more of the atoms in the ring is part of an amide group.

Lactams

Cyclic amides formed from the reaction between an amino group and a carboxylic acid group within the same molecule.