Question

Consider the following data of the number of hours 12 students spent online during the weekend and the scores of each student who took a test the followingMonday. Hrs spent online(x): 0 1,2,3,3,5,5,5,6,7,7,10. Test scores(y): 96,85,82,74,95,68,76,84,58,65,75,50.a. Find the sample linear correlation coefficient and interpret it. b. Is the population correlation coefficient significant? [ use ? = 0.05]. c. Find the equation of the regression line. What is the slope of the line? Interpret this value in the context? d. What is the coefficient of determination? Interpret the result? e. If ?? is 3.5 hours, what would you expect ?? to be? f. If ?? is 5 hours, what would you expect ?? to be? g. If ?? is 20 hours, what would you expect ?? to be? Show all work.

Answer 1

a)

correlation coefficient r=-0.8313

as correlation coeffficient is negative and its absolute value is near to 1; therefore it shows a strong negative relationship between  number of hours  spent online during the weekend and the scores of who took a test the followingMonday

b)

as test statistic from above test is in rejection reion we reject null hypothesis

and conclude that population correlation coefficient is significant

c)equation of the regression line:Yhat=93.9700-4.0674x

slope of the line =-4.0674

this can be interpreted as with each 1 hrs spent increase in online during the weekend score on average decrease by -4.0674.

d)coefficient of determination=r² =0.6911

this show that 69.1% variation in scores can be explained by variation in number of hours spent online during the weekend

e)

at x=3.5 ; predicted score =93.9700-4.0674*3.5=79.7341

f)

at x=5 ; predicted score =93.9700-4.0674*3.5=73.633

f)

at x=20 ; predicted score =93.9700-4.0674*20=12.6220

( however as x=20 does not lie in range of sampled values; it is not good to predict score due to extrapolation)