Answer:
Step-by-step explanation:
Given the data showing the relationship between GPA and hours of study :
From the regression model given :
Regression equation is:
y = 0.141x + 1.096
Also, the regression Coefficient, R = 0.957
Step-by-step explanation:
a) Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between the two variables on your graph.
From the regression equation, we can infer if the relationship or correlation between the two variables is positive or negative from the value of the slope, a positive slope Value means a positive relationship while a negative slope value means a negative relationship.
The Correlation Coefficient, R also gives the strength of relationship, with values close to - 1 or 1 depicting a strong relationship while positive and negative R values also depictava positive or negative relationship.
Here there is a strong positive relationship between GPA and Hours.
Correlation does not imply causation. Correlation only shows the type of relationship between variables and it does not mean that high GPA values are causes by long hours of study and vice versa
b)
A) The line of best fit gives a general outlook on the data while the correlation is the exact points showcased to calculate or show for a data set or table.
B) Between the two variables it is a positive correlation because they both increase in the same direction. Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction.
C) Not really considering the fact they are both headed in the same direction. It would if say one was increasing and the other was going in the opposite direction.
D) So, to find the residual I would subtract the predicted value from the measured value
E)
Ex: (Your first row)
9.2 - 2.23 = 6.97
c)
No, we can never tell that correlation is equal to causation. It is a common misconception when looking at data tables.
For instance, if we have a table that shows a correlation of scores on two tests in a row. We may see that there is a correlation between the two numbers. Students who did well on the first test may have done well on the second as well, and those who have not done well on the first may have done poorly on the second.
However, doing bad on the first test does not cause someone to do bad on the second one. Likely the cause is their studying habits, intelligence or aptitude in the area.
So in this example, there is correlation between the sets of data, but it does not prove causation.
d)
A residual is the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). It is the vertical distance from the actual plotted point to the point on the regression line.
e)
Answer:
the residual is 0
Step-by-step explanation:
The residual is zero because you don't have a trend line. Once you have a trend line the residual is the distance between the y-values(data or dots) and the trend line
f)
The estimated GPA of a student who studies for 15 hours a week is 3.21.
Given:
The table with the GPA of students along with the studying hours of students.
To find:
The residual plot for the given data.
GPA of a student who studies for 15 hours a week.
Solution:
The residual plot of the given data is an image attached.
The equation from the plot:
Where:
x = Hours of studies
y = GPA of student
If the student studies for 15 hours his or her GPA can be estimated as:
The estimated GPA of a student who studies for 15 hours a week is 3.21.
