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:

Low-income Families

Households with income levels significantly below the national average, often facing financial stress and limited access to resources.

Stressful Behaviors

Actions or responses exhibited by individuals when they are under stress, which can be detrimental to their health or well-being.

Parenting Program

Structured initiatives or workshops aimed at helping parents acquire skills and strategies to raise their children effectively.

Misbehaviors

Actions or conduct judged to be wrong or unacceptable by societal standards.