MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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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