statistic problem

this provision is restraint congeniality code on Rstudio, and propose in “html”

Problem 1
The designation “Multiple Direct Retreat restraint Lake Ice and Lake Clime Characteristics” by Gao & Stefan (1999) presents grounds on the consummation ice brawniness in mm (Thickness), mean estimate of days per year of ice clothe (DaysIceCover), mean estimate of days the moderate clime is bemoderate 8 degrees centrigrade (DaysLessThan8) and the mean snow profundity in mm (AvgSnowdepth) restraint 13 lakes in Minnesota. The grounds are in the file iceThickness.csv.

Construct a scatterconspire matrix restraint the unsteadys in this grounds. Describe/discuss the filthy unsteadys of the groundsset and any reputed intercommunitys you may look.
Match a multiple retreat example where Brawniness is the solution unsteady and the other three unsteadys are coercionebodeors
Assess the underlying assumptions restraint the example you match in 2.
Does the example (collectively) speakingly coercionebode the brawniness of the ice? (Justify by referencing inequitable output).
What percent of the unsteady in ice brawniness is illustrateed by the example? (intimation inequitable output)
Answer the doubt: Do lakes with main mean snow profundity verge to accept main or lesser consummation ice brawniness?
In discourseing this doubt delight illustrate your affinitynale and any limitations/caveats in your solution.

Problem 2
The SAT is a standardized nursery penetration exam fascinated by numerous eminent ground tyros despite the United Avows. In undeniable climes, the SAT is a received exam used in nursery admissions, timeliness in other climes the ACT or other metrics are used restraint nursery admissions. Thus, the percentage of tyros preamble the SAT varies greatly by avow and clime. The file stateSATscores.csv contains mean SAT mandibles restraint each of the 50 avows in the USA restraint the year 1997 parallel with distinct other unsteadys (Avow name; Worth – worth per learner in mean daily retinue in notorious constituent and resultant grounds; PT.Affinity – the mean learner to teachmistress affinity in notorious grounds; Allowance – the estimated mean allowance of notorious ground teachmistresss in the avow; PercentSAT – the percentage of tyros electing to choose the SAT exam; Verbal – the mean Verbal composite mandible; Math – the mean Mathematics composite mandible; and SAT – the mean composite SAT mandible).
Perform the controlthcoming with this grounds:

Construct a scatterconspire where the x-axis it the Percent preamble the SAT exam and the y-axis is the mean composite SAT mandible. Describe the intercommunity you look.
Match a weak direct retreat example where the solution is the composite SAT mandible and the coercionebodeor is the Percent of tyros preamble the SAT. Construct residual cue conspires of that match. What do you mark in the Residuals vs Matchted conspire?
Create a fantastic unsteady to the groundsset that is the clear rise of the Percent of Tyros preamble the SAT exam.
Match a multiple retreat example where the solution is the composite SAT mandible with span coercionebodeors: the percent of tyros preamble the exam and the clear rise of that percentage (the unsteady you created in deal-out 3). Construct residual cue conspires of that match. What do you mark in the Residuals vs Matchted conspire?
Determine if the matchted example in deal-out 4 is a speaking example to coercionebode composite SAT mandibles.  (intimation inequitable output)
What percentage of the variability in composite SAT mandibles is illustrateed by the example you match in deal-out 4? (intimation inequitable output)
We are assiduous in determining if tyro worths, learner-schoolmistress affinitys, and teachmistress allowance govern SAT mandibles when accounting restraint the percentage who choose the SAT. Match a multiple retreat example where the coercionebodeor unsteadys conceive the percent preamble the SAT, the clear rise of that percentage (created in deal-out 3), the worths, learner-schoolmistress affinity, and teachmistress allowance. Compare/contrast this matchted example to that in deal-out 4. Do you handle that worths, learner-schoolmistress affinitys or teachmistress allowance coercionebode SAT mandibles unintermittently accounting restraint the estimate of tyros preamble the SAT exam? Intimation inequitable output from the matchted example to discourse this doubt.

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