A Regression Was Performed on a Sample of 20 Observations

question 34

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.

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Definitions:

Epidemiology

The study and analysis of the distribution, patterns, and determinants of health and disease conditions in defined populations.

Prognosis

A prediction regarding the likely course and outcome of a disease or condition, based on medical knowledge and patient-specific factors.

Diagnosis

The process of identifying and determining the nature of a disease or disorder through evaluation of patient history, examination, and review of laboratory data.

Aetiology

The study of causes or origins, often used in the contexts of disease to describe the factors contributing to the onset of health conditions.