Question

thletes are constantly seeking measures of the degree of their cardiovascular fitness prior to the major race. Athletes want to know when their training is at a level which will produce a peak performance. One such measure of fitness is the time to exhaustion from running on a treadmill at a specified (?)angle and speed. The important question is then “Does this measure of cardiovascular fitness translates into performance in a 10-km running race?” (?)Twenty experienced distances runners who professed to be at the top condition were evaluated on the treadmill and then had their times recorded in a 10-km race. Use the following information, as necessary, to answer the following questions.

r= 0.82 xbar= 9.75 sx= 1.39 ybar= 40.80 sy= 3.31 sy/x= 1.92

a. Interpret the value of sample correlation coefficient . ?

b. Estimate alpha hat, beta hat, standard error, and their standard errors. Interpret beta hat in the context of the problem

.c. Write equation of regression line. Calculate and interpret the value of R square. What proportion of the variation in the data left unaccounted by the fitted regression line? Discuss the goodness of fit of the fitted straight line model based on the value of R square

d. Construct and interpret the 95% confidence interval for beta hat.

e.Test the appropriate hypotheses to see if there is a linear relationship between the amount of time needed to run a 10-km race and the time of exhaustion in the treadmill. Use Interpret your results.?=5%.f. Find the predicted values for treadmill times for X= Interprate the predicted value

Answer 1

d=139 g= 40.80 8y = 3,31 Y = 0,82 ū=9.75 sya=192 n=20 a) The There needed in the correlation (1) is a positive to run a treadmill. valore isi 8.82 with positive sign, Hanee, association between the amount of time 100km race and the time of exhaustion 5 beta hat (B) = x - 1.9.2 51.3813 1.39 Alphal hat ( = y bła 40.80-1.381389.75=27.3323 Standard enor () = 16+)3.32-1620-1) 1.927 V =3,0904 . (201) 1.392/20-2) Standard error of (2) & Sell Be sele) = oc/t to the one +30941, one 19x1.39² 1.7361 880) - Gelas 25.0904 9880450 ** (20-tal Toxinsan 50.5101 c) Thi regression line is 9=27.3323 +1.3813 x Co2 761) agus / massă (19x1.425/1921.392) 0.741 1943.312

The proportion of variation in the data left unaccounted by the fitted regression line is (1-0.1741)=0.8259. So only 17.41% variation of the model explained by the fitted regression line is not good enough for the model.

73. m. 78 sqmna d) 95% ef of beta is B is rebu Mlaine Graduate s tore fotbols wit" *1-0.05 20-2 SELB) = 1.38137 2.1009* 0.510 51-3813 E 1.0716 = (0.3097 2.4 529) (3) 12 Hypothesis Heiß=of is hieß to gjte Test statistic t= ß LESNO SE ) tome a p-value 2P(+72.70.84) - 1.3813 5 2.70841 ./ 0.510 at 184: = 0.014 lomas at mobive lawffins Clase mere is The p-value i u 0.0144 and greater than a Tacos 250.05. Henu, reject the null hypothesis and conclude that there is relationship between the amount of the needed to g. run a lookem raha race and the time of exhaustion in the treadmill, Op o le As - thomas- a lineas asolt