A Regression Was Performed on a Sample of 20 Observations $\hat { y }$

question 32

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. $\hat { y }$ = 23.72 + 12.61x + .798z
The standard errors for the coefficients are sb₁ = 4.85 and sb₂ = .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 multiple coefficient of determination and the adjusted multiple coefficient of determination. Interpret the meaning of the multiple coefficient of determination.
e.
Test the significance of the relationship among the variables at the 5% level of significance.

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Definitions:

Renal Calculi

Calcium stones in the renal pelvis.

Pressure Ulcers

A localized injury to the skin and/or underlying tissue, usually over a bony prominence, as a result of pressure, or pressure in combination with shear.

Thrombus Formation

The process of blood clotting inside a blood vessel, obstructing blood flow.

Body Alignment

The optimal placement of the body parts so that the bones are efficiently used, minimizing strain on the body and thereby reducing the risk of injury.