A study was done to look at the relationship between number of partners college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Partners 7 8 6 1 6 6 4...

A study was done to look at the relationship between number of partners college students have had in their lifetimes and their GPAs. The results of the survey are shown below.

1. Find the correlation coefficient:  r=r=    Round to 2 decimal places.


2. The null and alternative hypotheses for correlation are:
   H0:H0: ? r ρ μ Incorrect == 0
   
   Ha:Ha: ? r ρ μ Incorrect  ≠≠ 0


3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. You may want to reference the 95% Critical Values of the Sample Correlation Coefficient.
   
   
   
   

   
   
   • There is statistically insignificant evidence to conclude that there is a correlation between the number of partners students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate.
   
   
   • There is statistically significant evidence to conclude that a student who has had more partners will have a lower GPA than a student who has had fewer partners.
   
   
   • There is statistically insignificant evidence to conclude that a student who has had more partners will have a lower GPA than a student who has had fewer partners.
   
   
   • There is statistically significant evidence to conclude that there is a correlation between the number of partners students have had in their lifetimes and their GPA. Thus, the regression line is useful.
   
   

   
   Incorrect
   
   


4.  r2r2 = (Round to two decimal places)


5.  Interpret r2r2 :
   
   
   

   
   
   • Given any group of students who have all had the same number of partners, 71% of all of these studetns will have the predicted GPA.
   
   
   • 71% of all students will have the average GPA.
   
   
   • There is a 71% chance that the regression line will be a good predictor for GPA based on the number of partners a student has had.
   
   
   • 71% of the variation in students' GPAs can be explained by variation in the number of partners students have.
   
   

   
   Incorrect
   
   


6. The equation of the linear regression line is:
   ˆyy^ = xx +    (Please show your answers to two decimal places)
   
   
   
   
   


7. Use the model to predict the GPA of a college student who as had 6 partners.
   GPA = (Please round your answer to one decimal place.)
   
   
   
   
   


8. Interpret the slope of the regression line in the context of the question:
   
   
   

   
   
   • The slope has no practical meaning since a GPA cannot be negative.
   
   
   • For every additional partner students have, their GPA tends to decrease by 0.26.
   
   
   • As x goes up, y goes down.
   
   

   
   Correct
   
   
   
   
   
   


9. Interpret the y-intercept in the context of the question:
   
   
   

   
   
   • The best prediction for the GPA of a student who has never had a partner is 3.44.
   
   
   • The y-intercept has no practical meaning for this study.
   
   
   • If a student has never had a partner, then that student's GPA will be 3.44.
   
   
   • The average GPA for all students is predicted to be 3.44.
   
   

   
   Correct