Question
Use the given scatter plots to answer the questions.
a) Does this scatter plot show a positive association, negative association, or non-association? Explain why.
b) Is there an outlier in this data set? If so, approximately how old is the outlier and how about many minutes does he or she study per day?
c) Is this association linear or non-linear? Explain why.
d) What can you say about the relationship between your age and the amount that you study?
Hint:
An outlier for a scatter plot is the point that is farthest from the regression line.
If the trend line has a positive slope, then the scatter plot has a positive association.
We are asked to check whether the association is positive or negative, existence of an outlier, the behavior of the graph and the relationship between the data set.
The correct answer is: We are asked to check whether the association is positive or negative, existence of an outlier, the behavior of the graph and the relationship between the data set.
ANSWER:
Step 1 of 4:
The trend line corresponding to the scatter plot is:
Here, the slope of the trend line is positive. Hence, the corresponding association is positive.
That is, the scatter plot has a positive association.
Step 2 of 4:
Yes, there exists an outlier in the scatter plot.
The student is 12 years old and spends approximately 75 minutes to study.
Step 3 of 4:
The given graph shows a linear behavior. A particular nonlinearity or curvature cannot be observed in the graph. Moreover, a trend line can be approximated for the scatter plot, which is possible for a linear graph.
Step 4 of 4:
It is clearly evident form the graph that as the age increases, the time devoted to study also increases gradually.
That is, they are directly proportional. Hence, we can say that the set of data has positive linear relation.
Here, the slope of the trend line is positive. Hence, the corresponding association is positive.
That is, the scatter plot has a positive association.
Step 2 of 4:
Yes, there exists an outlier in the scatter plot.
The student is 12 years old and spends approximately 75 minutes to study.
Step 3 of 4:
The given graph shows a linear behavior. A particular nonlinearity or curvature cannot be observed in the graph. Moreover, a trend line can be approximated for the scatter plot, which is possible for a linear graph.
Step 4 of 4:
It is clearly evident form the graph that as the age increases, the time devoted to study also increases gradually.
That is, they are directly proportional. Hence, we can say that the set of data has positive linear relation.
If a graph has a nonlinear behavior, then the points would be arranged in some sort of a curve. A slope is the measure of the steepness of a line.
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