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 output of the regression fit is shown below.

The guidance counselor wants to create a 90% prediction interval for the GPA of a student who is graduating with a percentile rank of 90 (i.e., in the top 10% of the class). What is the upper bound of this interval, to two decimal places? Use the fact that the average rank is 80.8 and with a standard deviation of 16.6. Use three decimal places for all calculations up to the answer. Hint: Use the prediction interval formula, not the confidence interval formula. If you have done the confidence interval formula question for this problem already, you can compare your answer here to the one earlier: the upper bound of the prediction interval will be larger than the upper bound for the confidence interval.

SUMMARY OUTPUT Regression Statistics Multiple R 0.42853296 R Square 0.183640498 Adjusted R Square 0.183443071 0.595165667 Standard Error 4137 Observations ANOVA df F Significance F SS MS Regression 1 329.487 329.487 930.1704 1.8886E-184 Residual 4135 1464.709 0.354222 Total 4136 1794.196 Coefficients tandard Em t Stat LP-value Lower 95% LUpper 95% 1.276896668 0.046049 27.72907 23E-155 1.186615795 1.367 177542 Intercept 0.017034905 0.000559 30.4987 1.9E-184 0.015939856 0.018129954 Percentile Rank

Explanation / Answer

Sol:

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)

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