Question

b) The tndents wh take erte run the print typicol lbe there hegatul havp sharter iwm So TOL O 1 Sprint (cecos Stats: correlation and Regressien Exercises _Dec102018 The table below shows data for 13 students in a statistics class. Each member of the class ran a 40-yard sprint and then did a long jump (with a running start). Sprint Time (s) 5.41 5.05 9.49 8.09 7.01 7.17 6.83 6.73 8.01 5.68 5.78 6.31 6.04 Long Jump (in) 171 184 48 151 90 65 94 78 71 130 173 143 141 a) Create and label a scatterplot of the data (Sprint time vs Long Jump) b) Describe and interpret the scatterplot above. c) Calculate the LSRL equation and the regression coefficient r and R?. What can you say about them? d) Plot the Residuals vs Long jump. e) Calculate the LSRL and regression coefficient of the Residuals.

Answer 1

a.

b. The scatterplot shows almost all points lying on a line with negative slope. This indicates a strong negative linear relationship between the variables Long jump and Sprint Time.

c. For the regression

Long jump=alpha+beta *Sprint time+error,

we get the estimates

beta_hat=rSD(Long jump)/SD(Sprint Time)=Cov(Long Jump,Sprint Time)/Var(Sprint Time)=-42.84519/1.550747=-27.629

alpha_hat= Mean(Long jump)-beta_hat*Mean(Sprint time)=118.3846+27.629*6.738462=304.560,

Thus the regression equation is

Long jump_hat=304.560-27.629 *Sprint time

The correlation coefficient between the variables, r= Cov(Long Jump,Sprint Time)/(SD(Sprint time)*SD(Long Jump))=-42.84519/( 1.24529* 46.05529)= -0.7470541

R^2=r^2= 0.5581

r is quite close to -1, indicating strong negative association between the variables. However R^2 is only 55.81%, which indicates only 55.81% variation in data is explained by the regression. Possibly there are some outliers decreasing the accuracy of the regression.

d)