A Regression Was Performed on a Sample of 20 Observations

question 103

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:

Tangentially Relevant

Pertains to a matter or subject that is slightly or indirectly related to the core issue or focus.

Statistics

The science dealing with the collection, analysis, interpretation, and presentation of numerical data.

Dissonance Theory

A psychological theory suggesting that individuals experience discomfort (dissonance) arising from inconsistent beliefs, attitudes, or behaviors and are motivated to reduce this discomfort by changing them to achieve consistency.

Enjoyable

Capable of providing pleasure or satisfaction, often used to describe experiences or activities.