A social scientist asked a random sample of 50 students, “How many friends do you have on your favorite social media site, and how many of them are meaningful?” The social scientist would like to know if there is convincing evidence of a linear relationship between the number of friends students have on their favorite social media site and the number of friends who are meaningful. The regression model conditions were checked and were determined to be met. A scatterplot and computer output are shown below. a) Using the regression output, write the equation of the least-squares regression line. Identify all variables used in the equation.
b) If a student has 400 more friends on their favorite social media site than the student’s cousin, how many additional friends are expected to mean something to that student?
The social scientist would like to test H0: β= 0 versus Ha: β≠ 0 where β= the slope of the regression line relatingy= the number of friends who mean something to x= the number of friends on the favorite social media site for the population of all students.
c) Is there statistically convincing evidence of a linear relationship between the number of friends a student has on their favorite social media site and the number of friends who mean something to them? Use = 0.01. Explain.