19 GPA and study time A survey was conducted on 218 undergra

1.9 GPA and study time. A survey was conducted on 218 undergraduates from Duke Uni- versity who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. https://www.openintro.org/download.php?file=os2_tablet&referrer=/stat/textbook.php

Graph is in P.46

a) What is the explanatory variable and what is the response variable?

(b) Describe the relationship between the two variables. Make sure to discuss un- usual observations, if any.

(c) Is this an experiment or an observa- tional study?

(d) Can we conclude that studying longer hours leads to higher GPAs?

Solution

(a) Explanatory: An explanatory variable is the one which explains the variation in other variable(response). Here, number of study hours per week is used as a explanatory to the GPA. So, the explanatory variable is - \"Number of study hours per week\" and Response variable is : \"GPA\".

(b) There is a slight positive relationship between the two variables. One respondent reported a GPA above 4.0, which is a data error. There are also a few respondents who reported unusually high study hours (60 and 70 hours/week). The variability in GPA also appears to be larger for students who study less than those who study more. Since the data become sparse as the number of study hours increases, it is somewhat dicult to evaluate the strength of the relationship and also the variability across dierent numbers of study hours.

(c) This is an Observational study because the conclusion are drawn using the observed data of students.

(d) Since this is an observational study, a causal relationship is not implied. So, we can\'t conclude that studying longer leads to higher GPA.