A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.Student Test Grade 1 Test Grade 21 42 812 51 743 88 624 99 575 54 726 66 737 87 638 99 579 97 5810 89 6311 42 7712 71 6313 96 5514 56 7615 75 6916 57 7017 62 7518 89 6319 50 7220 56 7221 89 57Step 1 of 2 : Using statistical software, estimate the parameters of the modelSecond Test Grade=β0+β1(First Test Grade)+εi.Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary. Below is the transcribed table of student test grades:| Student | First Test Grade | Second Test Grade ||---------|------------------|-------------------|| 1 | 42 | 81 || 2 | 51 | 74 || 3 | 88 | 62 || 4 | 99 | 57 || 5 | 54 | 75 || 6 | 66 | 73 || 7 | 87 | 63 || 8 | 99 | 58 || 9 | 97 | 58 || 10 | 89 | 63 || 11 | 42 | 77 || 12 | 71 | 63 || 13 | 96 | 76 || 14 | 56 | 76 || 15 | 75 | 69 || 16 | 56 | 70 || 17 | 62 | 75 || 18 | 89 | 63 || 19 | 52 | 79 || 20 | 56 | 72 || 21 | 89 | 57 |This table provides a comparison between the first and second test grades for 21 students. Each column represents a data set: the first column lists the student number, the second column lists the grades for the first test, and the third column lists the grades for the second test. This data can be used to analyze changes in student performance between the two tests. The image displays a mathematical equation template with two empty boxes ready for input:\[\hat{y}_i = \text{[empty box]} + (\text{[empty box]}) x_i\]This represents a linear equation where $\hat{y}_i$ is the predicted value, and $x_i$ is the independent variable. The first empty box would typically be filled with the intercept term, and the second box with the slope coefficient.

Name: A statistics professor would like to build a model relating student sc
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Description: A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.Student T

Here we are using R programming language statistical software-

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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A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.

Student Test Grade 1 Test Grade 2
1 42 81
2 51 74
3 88 62
4 99 57
5 54 72
6 66 73
7 87 63
8 99 57
9 97 58
10 89 63
11 42 77
12 71 63
13 96 55
14 56 76
15 75 69
16 57 70
17 62 75
18 89 63
19 50 72
20 56 72
21 89 57

Step 1 of 2 : Using statistical software, estimate the parameters of the model

Second Test Grade=β0+β1(First Test Grade)+εi.

Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Below is the transcribed table of student test grades:

| Student | First Test Grade | Second Test Grade |
|---------|------------------|-------------------|
| 1 | 42 | 81 |
| 2 | 51 | 74 |
| 3 | 88 | 62 |
| 4 | 99 | 57 |
| 5 | 54 | 75 |
| 6 | 66 | 73 |
| 7 | 87 | 63 |
| 8 | 99 | 58 |
| 9 | 97 | 58 |
| 10 | 89 | 63 |
| 11 | 42 | 77 |
| 12 | 71 | 63 |
| 13 | 96 | 76 |
| 14 | 56 | 76 |
| 15 | 75 | 69 |
| 16 | 56 | 70 |
| 17 | 62 | 75 |
| 18 | 89 | 63 |
| 19 | 52 | 79 |
| 20 | 56 | 72 |
| 21 | 89 | 57 |

This table provides a comparison between the first and second test grades for 21 students. Each column represents a data set: the first column lists the student number, the second column lists the grades for the first test, and the third column lists the grades for the second test. This data can be used to analyze changes in student performance between the two tests.

The image displays a mathematical equation template with two empty boxes ready for input:

\[
\hat{y}_i = \text{[empty box]} + (\text{[empty box]}) x_i
\]

This represents a linear equation where $\hat{y}_i$ is the predicted value, and $x_i$ is the independent variable. The first empty box would typically be filled with the intercept term, and the second box with the slope coefficient.

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