Analyzing the Relationship between Hours of Sleep and GPA - Prof. Patrick S. Murphy, Assignments of Data Analysis & Statistical Methods

Data on the hours of sleep and gpas of 18 students. The goal is to analyze the relationship between these two variables by interpreting the scatterplot, identifying outliers and influential observations, calculating the regression line equation, and making predictions about gpas based on hours of sleep. This information could be useful for students and educators to understand the impact of sleep on academic performance.

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Pre 2010

Uploaded on 08/03/2009

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Hours of Sleep
GPA
GPA versus Hours of Sleep
Suppose that you wanted to “explain” how the amount of sleep you get each night affects
your GPA. If you were to gather data of others GPA and hours of sleep, you might be
able to “predict” your GPA given the amount of sleep you get each night. Another way
of thinking about this is that GPA is a “response” to the hours of sleep you get. Below is
an example of data gathered on 18 students.
X is the Explanatory (or Predictor) variable
Y is the Response variable
When we say we are graphing “GPA versus Hours of Sleep” then
we are graphing “Y versus X”.
1. Describe the form and strength of the scatterplot.
2. State and interpret the association of these two variables.
Hour of Sleep
GPA
8 3.1
7 3.4
10 2.0
8 3.5
6 2.3
9 3.4
7 3.2
7 2.5
6 2.1
11 4.0
8 4.0
4 1.0
6 2.5
9 3.0
10 3.8
7 2.6
9 3.2
9 3.3
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Hours of Sleep

GPA

GPA versus Hours of Sleep

Suppose that you wanted to “explain” how the amount of sleep you get each night affects your GPA. If you were to gather data of others GPA and hours of sleep, you might be able to “predict” your GPA given the amount of sleep you get each night. Another way of thinking about this is that GPA is a “response” to the hours of sleep you get. Below is an example of data gathered on 18 students.

X is the Explanatory (or Predictor) variable Y is the Response variable

When we say we are graphing “GPA versus Hours of Sleep” then we are graphing “Y versus X”.

  1. Describe the form and strength of the scatterplot.
  2. State and interpret the association of these two variables.

Hour of Sleep GPA 8 3. 7 3. 10 2. 8 3. 6 2. 9 3. 7 3. 7 2. 6 2. 11 4. 8 4. 4 1. 6 2. 9 3. 10 3. 7 2. 9 3. 9 3.

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  1. State Outliers and Influential Observations, if any.
  2. What is the equation for the regression Line?
  3. Predict the GPA for a student that gets 10 hours of sleep each night.
  4. What GPA would you expect for a student that gets 8 hours of sleep each night?
  5. Predict the GPA for a student that gets 5 hours of sleep each night. Could you

figure this out from the table only?

  1. Interpret the slope of the regression line.