Answer:
Hence, the data provides convincing evidence that a linear relationship exists between hours of sleep observed and academic performance as measured by GPA.
Step-by-step explanation:
Given the data:
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7
The scatter plot shows a positive linear trend. With the correlation Coefficient depicting a R value of 0.56. The residual plot also depicts a a randomly scattered values of the residual values. Similarly, a plot of the normal values of residuals
The data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
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.
We have given data of the 14 seniors shown in the table.
To solve this question we will calculate the correlation coefficient 'r'
The formula for correlation coefficient :
[tex]\rm r =\frac{n\sum xy-\sum x \sum y}{\sqrt{[n\sum x^2-(\sum x)^2]}[n\sum y^2-(\sum y)^2]} }[/tex]
From the table the value of n = 14
[tex]\rm \sum x = 104.5[/tex] , [tex]\rm \sum y =47.7[/tex] , [tex]\rm \sum xy =357.8[/tex] , [tex]\rm \sum x^2 =797.25[/tex] , [tex]\rm \sum y^2 =163.09[/tex]
Put all the values in the above formula we get:
[tex]\rm r =\frac{14\times357.8-104.5 \times47.7}{\sqrt{[14\times 797.25-104.5^2][14\times163.09-47.7^2]} }[/tex]
[tex]\rm r = \frac{5009.2-4984.65}{\sqrt{(241.25)(7.97)} }[/tex]
[tex]\rm r = \frac{24.55}{43.849}[/tex]
r = 0.559 ≈ 0.56
The value of the correlation coefficient is 0.56 which is between the values 0.5 to 0.7 shows that the variables are moderately correlated.
Thus, the data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
Learn more about the correlation here:
brainly.com/question/11705632
