THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 18

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + ε ,where Y is the final mark (out of 100),X₁ is the number of lectures skipped,X₂ is the number of late assignments,and X₃ is the mid-term test mark (out of 100).The professor recorded the data for 50 randomly selected students.The computer output is shown below.
The regression equation is
= 41.6 - 3.18x₁ - 1.17x₂ + 0.63x₃.

S = 13.74 R-Sq = 30.0%
ANALYSIS OF VARIANCE

-Does the data provide enough evidence to conclude that,at the 5% significance level,the model is useful in predicting the final mark?

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Definitions:

Metencephalon

Second most posterior division of the embryonic brain; becomes the pons and cerebellum in the adult.

Cerebellum

A major structure of the hindbrain that controls fine motor skills, balance, and coordination.

Myelencephalon

The myelencephalon is a part of the brainstem, primarily responsible for controlling vital functions such as breathing, heart rate, and digestion.

Superior Colliculi

Paired structures located in the midbrain involved in visual processing, eye movements, and integrating sensory input with motor output.