A study was done to look at the relationship betweennumber of lovers college students have had in theirlifetimes and their GPAS. The results of the survey areshown below.Lovers45427GPA1.92.32.91.32.93.91.1a. Find the correlation coefficient: r =Round to 2 decimal places.b. The null and alternative hypotheses for correlationare:Но:?H1:?The p-value is:(Round to four decimalplaces)c. Use a level of significance of aconclusion of the hypothesis test in the context ofthe study.:0.05 to state theThere is statistically significant evidence toconclude that a student who has had morelovers will have a lower GPA than a studentwho has had fewer lovers.| There is statistically insignificant evidence toconclude that there is a correlation betweenthe number of lovers students have had intheir lifetimes and their GPA. Thus, the use ofthe regression line is not appropriate.There is statistically significant evidence toconclude that there is a correlation betweenthe number of lovers students have had intheir lifetimes and their GPA. Thus, theregression line is useful.| There is statistically insignificant evidence toconclude that a student who has had morelovers will have a lower GPA than a studentwho has had fewer lovers.d. 12:(Round to two decimal places)%3D e. Interpret r2 :There is a 87% chance that the regression linewill be a good predictor for GPA based on thenumber of lovers a student has had.87% of all students will have the average GPA.Given any group of students who have all hadthe same number of lovers, 87% of all of thesestudetns will have the predicted GPA.There is a large variation in students' GPAS,but if you only look at students who have hada fixed number of lovers, this variation onaverage is reduced by 87%.f. The equation of the linear regression line is:ŷ =x (Please show your+answers to two decimal places)g. Use the model to predict the GPA of a collegestudent who as had 6 lovers.GPA =(Please round your answer to onedecimal place.)h. Interpret the slope of the regression line in thecontext of the question:The slope has no practical meaning since aGPA cannot be negative.As x goes up, y goes down.For every additional lover students have,their GPA tends to decrease by 0.39.i. Interpret the y-intercept in the context of thequestion:| The y-intercept has no practical meaning forthis study.If a student has never had a lover, then thatstudent's GPA will be 3.88.The average GPA for all students is predictedto be 3.88.The best prediction for the GPA of a studentwho has never had a lover is 3.88.

a. Correlation coefficient measures the strength and direction of the linear relationship between…

A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAS. The results of the survey are shown below. Lovers 4 4 6 7 GPA 1.9 2.3 2.9 1.3 2.9 3.9 1.1 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Но: (? H1: (? The p-value is: (Round to four decimal places) c. Use a level of significance of a = conclusion of the hypothesis test in the context of the study. - 0.05 to state the | There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. |There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers 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 there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. |There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. d. p? = (Round to two decimal places) %3D

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 24PFA