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Problem 1
The season “Multiple Straight Retreat ce Lake Ice and Lake Sphere Characteristics” by Gao & Stefan (1999) presents postulates on the utmost ice density in mm (Thickness), mean reckon of days per year of ice secrete (DaysIceCover), mean reckon of days the dejected sphere is bedejected 8 degrees centrigrade (DaysLessThan8) and the mean snow profoundness in mm (AvgSnowdepth) ce 13 lakes in Minnesota. The postulates are in the file iceThickness.csv.

Construct a scatterconcoct matrix ce the unsteadys in this postulates. Describe/discuss the immodest unsteadys of the postulatesset and any reported interdependences you may perceive.
Adapt a multiple retreat example where Density is the defense unsteady and the other three unsteadys are prophesyors
Assess the underlying assumptions ce the example you adapt in 2.
Does the example (collectively) speakingly prophesy the density of the ice? (Justify by referencing separateicular output).
What percent of the unsteady in ice density is expounded by the example? (intimation separateicular output)
Answer the topic: Do lakes with superior mean snow profoundness incline to bear superior or lesser utmost ice density?
In harangueing this topic content expound your connectionnale and any limitations/caveats in your defense.

Problem 2
The SAT is a standardized beholdd-concoct portal exam engagen by multifarious tall teach tyros across the United Declares. In sure climes, the SAT is a favorite exam used in beholdd-concoct admissions, period in other climes the ACT or other metrics are used ce beholdd-concoct admissions. Thus, the percentage of tyros portico the SAT varies very-much by declare and clime. The file stateSATscores.csv contains mean SAT beaks ce each of the 50 declares in the USA ce the year 1997 concurrently with sundry other unsteadys (Declare name; Outgoings – outgoings per scholar in mean daily carriage in national constituent and minor teachs; PT.Connection – the mean scholar to educationist connection in national teachs; Hire – the estimated mean hire of national teach educationists in the declare; PercentSAT – the percentage of tyros electing to engage the SAT exam; Verbal – the mean Verbal composite beak; Math – the mean Mathematics composite beak; and SAT – the mean composite SAT beak).
Perform the aftercited with this postulates:

Construct a scatterconcoct where the x-axis it the Percent portico the SAT exam and the y-axis is the mean composite SAT beak. Describe the interdependence you perceive.
Adapt a mere straight retreat example where the defense is the composite SAT beak and the prophesyor is the Percent of tyros portico the SAT. Construct residual cue concocts of that adapt. What do you give-heed-to in the Residuals vs Adaptted concoct?
Create a innovating unsteady to the postulatesset that is the clear rise of the Percent of Tyros portico the SAT exam.
Adapt a multiple retreat example where the defense is the composite SAT beak with two prophesyors: the percent of tyros portico the exam and the clear rise of that percentage (the unsteady you created in separate 3). Construct residual cue concocts of that adapt. What do you give-heed-to in the Residuals vs Adaptted concoct?
Determine if the adaptted example in separate 4 is a speaking example to prophesy composite SAT beaks.  (intimation separateicular output)
What percentage of the variability in composite SAT beaks is expounded by the example you adapt in separate 4? (intimation separateicular output)
We are careful in determining if tyro outgoingss, scholar-educationist connections, and educationist hire bias SAT beaks when accounting ce the percentage who engage the SAT. Adapt a multiple retreat example where the prophesyor unsteadys involve the percent portico the SAT, the clear rise of that percentage (created in separate 3), the outgoingss, scholar-educationist connection, and educationist hire. Compare/contrast this adaptted example to that in separate 4. Do you reach that outgoingss, scholar-educationist connections or educationist hire prophesy SAT beaks uniformly accounting ce the reckon of tyros portico the SAT exam? Intimation separateicular output from the adaptted example to harangue this topic.

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