A Multiple Regression Was Performed on a Sample of 16 $\hat { y }$

question 90

Essay

A multiple regression was performed on a sample of 16 observations.The estimated equation is $\hat { y }$ = 23.5 - 14.28x₁ + 6.72x₂ + 15.68x₃.The standard errors for the coefficients are sb₁ = 4.2, sb₂ = 5.6, and sb₃ = 2.8.For this model, SST = 3809.6 and SSR = 3285.4.
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a.
Compute the appropriate t ratios.
b.
Test for the significance of β₁, β₂, and β₃ at the 5% level of significance.
c.
Do you think any of the variables should be dropped from the model? Explain.
d.
Compute R² and $R _ { \mathrm { a } } ^ { 2 }$ . Interpret R².
e.
Test the significance of the relationship among the variables at the 5% level of significance.

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Definitions:

Posterior Tibial Pulse

The pulse felt over the posterior tibial artery, located behind the inner ankle, which can provide information about circulatory health.

Dependent Position

A body position that is lower than the heart, often used to describe the positioning of limbs for medical examination or procedures.

Thready

Describes a weak and barely palpable pulse that feels thin and feeble, often indicating a decrease in the volume or force of the heart's contractions.

Phlebotomies

A medical procedure that involves the drawing of blood from a vein, typically for diagnostic or therapeutic purposes.