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:

Red-Figure Technique

An ancient Greek method of vase painting that featured red figures against a black background.

Andokides Painter

The Andokides Painter is an anonymous ancient Greek vase painter, active from approximately 530 to 515 BC, closely associated with the invention of the red-figure pottery technique.

Exekias

An ancient Greek potter and painter, renowned for his work in black-figure pottery painting during the 6th century B.C.

Caryatid

A female figure that functions as a supporting column. See also atlantid.