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It is believed that standardized test scores, such as the SAT, are a good predictor of first-year college students’ GPA.

x y

1200 1120

1000 1420

1280 750

1100 3.2

2.5 2.7

3.5 2.9

2.2 2.3

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01:40

It is believed that standardized test scores, such as the SAT, are a good predictor of first-year college students’ GPA.

x:120011201000142012807501100

y:3.22.52.73.52.92.22.3

Find the correlation coefficient. Round your final answer to four decimal places.r =

Write the regression equation below. Round all numbers to four decimal places.Å· =

Using the data shown above, predict a student’s first-year GPA when the student scores 1275 on the SAT. Round your final answer to two decimal places.

What percentage of variation in GPAs can be explained by students’ SAT scores? Round your final answer to two decimal places.%

03:53

Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Suppose the entering freshmen at a certain college have mean combined SAT Scores of $1222,$ with a standard deviation of $123 .$ In the first semester, these students attained a mean $G P A$ of $2.66,$ with a standard deviation of $0.56 .$ Ascatterplot showed the association to be reasonably linear, and the correlation between $S A T$ score and $G P A$ was 0.49 .a) Write the equation of the regression line.b) Explain what the $y$ -intercept of the regression line indicates.c) Interpret the slope of the regression line.d) Predict the GPA of a freshman who scored a combined 1400e) Based upon these statistics, how effective do you think SAT scores would be in predicting academic success during the first semester of the freshman year at this college? Explain.f) As a student, would you rather have a positive or a n…

01:22

A university conducted an analysis of the relationship between Math SAT scores (ranging from 200 to 800) and first-year GPAs (ranging from 0 to 4.0) for students who completed their first year. The average SAT score is 540 with a standard deviation (SD) of 78, and the average GPA is 2.5 with a SD of 0.55. The correlation coefficient is found to be 0.75.

a) If a student is chosen at random and has an SAT score of 652, use regression to predict this student’s GPA.b) Assuming that both SAT scores and GPAs follow a normal distribution, predict the percentile rank of another student’s GPA given that their SAT percentile rank is 91.15 percent.

03:30

Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Suppose the entering freshmen at a certain college have mean combined SAT Scores of 1833 , with a standard deviation of 123 . In the first semester these students attained a mean GPA of $2.66$, with a standard deviation of $0.56 .$ A scatterplot showed the association to be reasonably linear, and the correlation between $S A T$ score and $G P A$ was $0.47$.a) Write the equation of the regression line.b) Explain what the $y$ -intercept of the regression line indicates.c) Interpret the slope of the regression line.d) Predict the GPA of a freshman who scored a combined $2100 .$e) Based upon these statistics, how effective do you think SAT scores would be in predicting academic success during the first semester of the freshman year at this college? Explain.f) As a student, would you rather have a positive or a nega…

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