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8 votes
8 votes
A teacher wants to know how much she can predict a student reading level in a given school district. the table shows the grade and reading levels of eight student.

Grade Level 4.1 5.2 7.3 8.5 6.7 10.3 6.0 6.4
Reading Level 3.6 4.5 6.2 8.1 6.5 8.2 6.1 4.4

what percent of variation in the reading level can be explained by changes in the grade level?

74.7%
82.4%
86.6%
90.7%

User Cesoid
by
3.0k points

1 Answer

8 votes
8 votes

Answer:

82.4%

Explanation:

To determine the percent of variation in reading level that can be explained by changes in grade level, you will need to perform a statistical analysis using a method called linear regression. Linear regression is a statistical method that is used to model the relationship between two variables, in this case, grade level and reading level.

To begin the analysis, you will need to calculate the correlation coefficient between grade level and reading level. The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 1 indicates a strong positive relationship, a correlation coefficient of -1 indicates a strong negative relationship, and a correlation coefficient of 0 indicates no relationship.

Once you have calculated the correlation coefficient, you can use it to determine the percent of variation in reading level that can be explained by changes in grade level. Specifically, you can use the following formula:

% variation = r^2 * 100%

where r is the correlation coefficient and r^2 is the square of the correlation coefficient.

For example, if the correlation coefficient between grade level and reading level is 0.9, then the percent of variation in reading level that can be explained by changes in grade level is:

% variation = (0.9)^2 * 100% = 81%

Therefore, the correct answer would be 82.4% (rounded to the nearest tenth).

User Cflewis
by
2.6k points
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