A guidance counselor at a local high school is interested in determining what, i

Question

A guidance counselor at a local high school is interested in determining what, if any, linear relationship there is between high school percentile ranks and college GPAs. A student's percentile rank is calculated by determining the percentage of all students in the graduating class with a final high school GPA at or below his or hers. For example, a student graduating 10th in a class of 300 would have a percentile rank (to one decimal place) of (290/300)x100 = 96.7.

The guidance counselor fits the model in Excel and obtains the following output:

The guidance counselor wants to create a 90% confidence interval for the mean GPA of students who graduate at the 90th percentile (i.e., at the top 10% of their class). That is, you are looking to find an interval for E(GPA|Percentile_Rank = 90).

Explanation / Answer

from regression eq

GPA=1.277+0.017(percentile_rank)

for percentile rank 90

GPA=1.277+0.017(90)

GPA=2.807

GPA=2.81(round to 2 decimals as required)

The interpretation about R2 is, About 82% or higher of the variability in college GPAs can be "explained," or accounted for, by the regression fit between college GPA and high school percentile rank.- this gives us the interpretation of ggod fit.

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