A Regression Was Performed on a Sample of 20 Observations

question 129

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. 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.

---

Definitions:

Lower-order Needs

Basic physiological and safety needs at the bottom levels of Maslow’s hierarchy, which must be satisfied before higher-level needs can be addressed.

Maslow

Refers to Abraham Maslow, a psychologist known for creating Maslow's hierarchy of needs, a theory in psychology that prioritizes human needs from basic to self-fulfillment.

Physiological

Relating to the functions and processes that occur within living organisms, especially in terms of how they support life and health.

Esteem

The regard in which an individual or entity is held by others; often related to respect and admiration.