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A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless attempt to predict performance in college from performance on this test. We have chosen a random sample of students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600) and her grade point average (from 0 to 4) for her first year in college. The data are shown below, with x denoting the score on the standardized test and y denoting the first-year college grade point average. The least-squares regression line for these data is y = 1.1279+0.0015x. This line is shown in the scatter plot below. Standardized Grade point average, test score, X 1010 3.08 900 2.82 1260 3.34 36- 1510 3.48 34- 1100 2.32 32- S70 2.27 1360 3.59 28- 26- 800 2.35 24- 940 2.19 22- 1060 2.90 1210 2.73 1490 3.06 12 isie 990 2.37 Standardized test score, X 1390 2.98 1280 3.06 Send data to calculator Send data to Excel Based on the sample data and the regression line, complete the following. (a) For these data, standardized test scores that are greater than the mean of the standardized test scores tend to be paired with grade point averages that are (Choose one) |the mean of the grade point averages. (b) According to the regression equation, for an increase of one point in standardized test score, there is a corresponding increase of how many points in grade point average? () From the regression equation, what is the predicted grade point average when the standardized test score is 1510? (Round your answer to at least two decimal places.) Gra de point average, y

A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless attempt to predict performance in college from performance on this test. We have chosen a random sample of students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600) and her grade point average (from 0 to 4) for her first year in college. The data are shown below, with x denoting the score on the standardized test and y denoting the first-year college grade point average. The least-squares regression line for these data is y = 1.1279+0.0015x. This line is shown in the scatter plot below. Standardized Grade point average, test score, X 1010 3.08 900 2.82 1260 3.34 36- 1510 3.48 34- 1100 2.32 32- S70 2.27 1360 3.59 28- 26- 800 2.35 24- 940 2.19 22- 1060 2.90 1210 2.73 1490 3.06 12 isie 990 2.37 Standardized test score, X 1390 2.98 1280 3.06 Send data to calculator Send data to Excel Based on the sample data and the regression line, complete the following. (a) For these data, standardized test scores that are greater than the mean of the standardized test scores tend to be paired with grade point averages that are (Choose one) |the mean of the grade point averages. (b) According to the regression equation, for an increase of one point in standardized test score, there is a corresponding increase of how many points in grade point average? () From the regression equation, what is the predicted grade point average when the standardized test score is 1510? (Round your answer to at least two decimal places.) Gra de point average, y

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Website: Analysis of Standardized Test Scores and College GPA** A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but it can still predict performance in college to some extent. We randomly selected students who finished their first year of college, recorded their test scores (ranging from 400 to 1600), and noted their first-year GPA (on a 0 to 4 scale). ### Data Table The data set of standardized test scores (x) and corresponding GPAs (y) is as follows: | Standardized test score, x | Grade point average, y | |----------------------------|------------------------| | 1010 | 3.08 | | 900 | 2.32 | | 1260 | 3.22 | | 1000 | 2.84 | | 1510 | 3.48 | | 1300 | 3.12 | | 920 | 1.96 | | 800 | 2.35 | | 940 | 2.19 | | 1060 | 2.90 | | 1210 | 2.73 | | 1490 | 3.06 | | 990 | 2.37 | | 1390 | 2.98 | | 1280 | 3.06 | ### Scatter Plot and Regression Line The scatter plot shows the relationship between standardized test scores and GPAs. The plotted points indicate individual student data. The graph includes a least-squares regression line, \( \hat{y} = 1.1279 + 0.0015x \), suggesting a positive correlation between the test scores and GPAs. ### Analysis Questions Based on the data and regression line: (a) For test scores greater than the mean, the corresponding GPAs tend to be (Choose one: above/below/equal to) the mean GPA. (b) According to the regression equation, an increase of one point in the test score corresponds to an increase in GPA by approximately 0.0015 points. (c) To predict the GPA when the test score is 1510, use the regression equation: \( \hat{y} = 1.1279 + 0.0015(1510
Transcribed Image Text:**Educational Website: Analysis of Standardized Test Scores and College GPA** A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but it can still predict performance in college to some extent. We randomly selected students who finished their first year of college, recorded their test scores (ranging from 400 to 1600), and noted their first-year GPA (on a 0 to 4 scale). ### Data Table The data set of standardized test scores (x) and corresponding GPAs (y) is as follows: | Standardized test score, x | Grade point average, y | |----------------------------|------------------------| | 1010 | 3.08 | | 900 | 2.32 | | 1260 | 3.22 | | 1000 | 2.84 | | 1510 | 3.48 | | 1300 | 3.12 | | 920 | 1.96 | | 800 | 2.35 | | 940 | 2.19 | | 1060 | 2.90 | | 1210 | 2.73 | | 1490 | 3.06 | | 990 | 2.37 | | 1390 | 2.98 | | 1280 | 3.06 | ### Scatter Plot and Regression Line The scatter plot shows the relationship between standardized test scores and GPAs. The plotted points indicate individual student data. The graph includes a least-squares regression line, \( \hat{y} = 1.1279 + 0.0015x \), suggesting a positive correlation between the test scores and GPAs. ### Analysis Questions Based on the data and regression line: (a) For test scores greater than the mean, the corresponding GPAs tend to be (Choose one: above/below/equal to) the mean GPA. (b) According to the regression equation, an increase of one point in the test score corresponds to an increase in GPA by approximately 0.0015 points. (c) To predict the GPA when the test score is 1510, use the regression equation: \( \hat{y} = 1.1279 + 0.0015(1510
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