**Understanding the Relationship Between Homework and Final Grades**Students at a local university believe that their statistics instructor assigns extensive homework to penalize them. They wonder if there is a relationship between the number of optional homework problems they complete during the semester and their final grades. The students decide to track the number of these problems completed throughout the semester, recording each student's total and their final grade at the end.**Research Question:**What is the regression equation to predict the final grade from the number of homework assignments completed?**Data Table:**| Problems (X) | Grade (Y) | (X-Ō) | (Y-Ȳ) | (X-Ō)(Y-Ȳ) | (X-Ō)² | (Y-Ȳ)² ||--------------|----------|-------|-------|------------|--------|--------|| 51 | 62 | -21.75| -8.67 | 188.57 | 473.06 | 75.17 || 58 | 68 | -14.75| -2.70 | 39.83 | 217.56 | 7.29 || 62 | 66 | -10.75| -4.67 | 50.20 | 115.56 | 21.81 || 65 | 66 | -7.75 | -4.67 | 36.19 | 60.06 | 21.81 || 68 | 67 | -4.75 | -3.67 | 17.43 | 22.56 | 13.47 || 76 | 72 | 3.25 | 1.33 | 4.32 | 10.56 | 1.77 || 77 | 73 | 4.25 | 2.33 | 9.90 | 18.06 | 5.43 || 78 | 72 | 5.25 | 1.33 | 6.98 | 27.56 | 1.77 || 78 | 78 | 5.25 | 7.33 | 38.48

The given data represents that the final grade and the number of problems assigned for homework.The regression line of y based on x is y = a + bx. Calculate the regression line of y based on x is as follows: Therefore, the regression line of y based on x is y = 44.8040 + 0.3555x.

Math

Statistics

Students at a local university believe that their statistics instructor gives them homework assignments just to punish them. They wonder if there is any relationship between the number of optional homework problems they do during the semester and their final course grade. They decide to keep track of the number of these problems completed during the course of the semester. At the end of the class each student's total is recorded along with their final grade. What is the regression equation to predict the final grade from the number of homework assignments completed? Problems Grade (X-X) (Y-Y) (X-X)(Y-Y) (X-X)? (Y-Y)² Y 51 62 -21.75 -8.67 188.57 473.06 75.17 58 68 -14.75 -2.7 39.83 217.56 7.29 62 66 -10.75 -4.67 50.20 115.56 21.81 65 66 -7.75 -4.67 36.19 60.06 21.81 68 67 -4.75 -3.67 17.43 22.56 13.47 76 72 3.25 1.33 4.32 10.56 1.77 77 73 4.25 2.33 9.90 18.06 5.43 78 72 5.25 1.33 6.98 27.56 1.77 78 78 5.25 7.33 38.48 27.56 53.73 84 73 11.25 2.33 26.21 126.56 5.43 85 76 12.25 5.33 65.29 150.06 28.41 91 75 18.25 4.33 79.02 333.06 18.75 873 848 562.44 1582.25 254.83

Students at a local university believe that their statistics instructor gives them homework assignments just to punish them. They wonder if there is any relationship between the number of optional homework problems they do during the semester and their final course grade. They decide to keep track of the number of these problems completed during the course of the semester. At the end of the class each student's total is recorded along with their final grade. What is the regression equation to predict the final grade from the number of homework assignments completed? Problems Grade (X-X) (Y-Y) (X-X)(Y-Y) (X-X)? (Y-Y)² Y 51 62 -21.75 -8.67 188.57 473.06 75.17 58 68 -14.75 -2.7 39.83 217.56 7.29 62 66 -10.75 -4.67 50.20 115.56 21.81 65 66 -7.75 -4.67 36.19 60.06 21.81 68 67 -4.75 -3.67 17.43 22.56 13.47 76 72 3.25 1.33 4.32 10.56 1.77 77 73 4.25 2.33 9.90 18.06 5.43 78 72 5.25 1.33 6.98 27.56 1.77 78 78 5.25 7.33 38.48 27.56 53.73 84 73 11.25 2.33 26.21 126.56 5.43 85 76 12.25 5.33 65.29 150.06 28.41 91 75 18.25 4.33 79.02 333.06 18.75 873 848 562.44 1582.25 254.83

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

**Understanding the Relationship Between Homework and Final Grades**

Students at a local university believe that their statistics instructor assigns extensive homework to penalize them. They wonder if there is a relationship between the number of optional homework problems they complete during the semester and their final grades. The students decide to track the number of these problems completed throughout the semester, recording each student's total and their final grade at the end.

**Research Question:**
What is the regression equation to predict the final grade from the number of homework assignments completed?

**Data Table:**

| Problems (X) | Grade (Y) | (X-Ō) | (Y-Ȳ) | (X-Ō)(Y-Ȳ) | (X-Ō)² | (Y-Ȳ)² |
|--------------|----------|-------|-------|------------|--------|--------|
| 51 | 62 | -21.75| -8.67 | 188.57 | 473.06 | 75.17 |
| 58 | 68 | -14.75| -2.70 | 39.83 | 217.56 | 7.29 |
| 62 | 66 | -10.75| -4.67 | 50.20 | 115.56 | 21.81 |
| 65 | 66 | -7.75 | -4.67 | 36.19 | 60.06 | 21.81 |
| 68 | 67 | -4.75 | -3.67 | 17.43 | 22.56 | 13.47 |
| 76 | 72 | 3.25 | 1.33 | 4.32 | 10.56 | 1.77 |
| 77 | 73 | 4.25 | 2.33 | 9.90 | 18.06 | 5.43 |
| 78 | 72 | 5.25 | 1.33 | 6.98 | 27.56 | 1.77 |
| 78 | 78 | 5.25 | 7.33 | 38.48

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