Respuesta :
Ok, so to see which data sets is reasonable for a linear regression model square each set and if it is close to one it will be reasonable.
[tex]r^{2}[/tex]
9th grade 0.3 = [tex]0.3^{2}[/tex] = 0.09
10th grade –0.1 = [tex]-0.1^{2}[/tex] = 0.01
11th grade 0.2 = [tex]0.2^{2}[/tex] = 0.04
12th grade –0.8 = [tex]-0.8^{2}[/tex] = 0.64
So 12th grade data set is reasonable but the others are not because they are not remotely close to 1.
[tex]r^{2}[/tex]
9th grade 0.3 = [tex]0.3^{2}[/tex] = 0.09
10th grade –0.1 = [tex]-0.1^{2}[/tex] = 0.01
11th grade 0.2 = [tex]0.2^{2}[/tex] = 0.04
12th grade –0.8 = [tex]-0.8^{2}[/tex] = 0.64
So 12th grade data set is reasonable but the others are not because they are not remotely close to 1.
The 12th-grade data set represents the linear regression because the value of the correlation coefficient for the 12th-grade students is near the -1 which shows a perfect negative linear regression
What is correlation?
It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
The correlaton coeffiecient is given as below:
For 9th grade = 0.3
For 10th grade = -0.1
For 11th grade = 0.2
For 12th grade = -0.8
We know that for perfect linear regression the value of the correlation coefficient is 1 or -1
As we can see from the data given the nearest value of the correlation coefficient is -0.8 which is the correlation coefficient for the 12th grade.
Thus, the 12th-grade data set represents the linear regression because the value of the correlation coefficient for the 12th-grade students is near the -1 which shows a perfect negative linear regression.
Learn more about the correlation here:
brainly.com/question/11705632
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