Statistics...?

Question

Is there a relationship between how many sit-ups you can do and how fast you can run 40 yards?

a. The regression equation is 6.71 - 0.024x. Find the predicted time in the 40-yard dash for a subject who can do (i) 10 sit-ups, (ii) 40 sit-ups.

b. Interpret the y-intercept and slope of the equation in (a), in context.

c. Based on the slope in (a), is the correlation positive, or negative? Explain.

Answer 1

a. 6.47, 5.75

b. The y-int is the time it would take for a person to do the dash that could do no sit-ups. The slope is the (negative) effect on time that the ability to do each additional sit-up has.

c. Negative. For each additional sit-up that a person can do, their dash speed will decrease by 0.024 sec.

Answer 2

a)

for 10 sit ups, plug in x = 10 into the regression equation
6.71 - 0.024 * 10 = 6.47 sec

for 40 sit ups, plug in x = 40 into the regression equation
6.71 - 0.024 * 40 = 5.75

b)

the y-intercept is the expected time to run 40 yards for a person who cannot do a single situp.

the slope is the number of seconds the 40-yard time is reduced on average for every sit up a person can do.

c)

the correlation is negative. the time decreases as the number of sit ups increases.

a positive correlation would be an increase in time as sit ups increases.

Answer 3

a) 6.71 - .024(10) and 6.71 - .024(40)

b) 6.71/0.024 this is the number of situps you need to be able to do inorder to be expected to be able to instantaneously run 40 yards (HA!!!!!)

c) slope (Beta) is -.024 negative correlation between time of run and num sittups

P.S. this problem is retarded any real statistician wouldn't think this way. a much more reasonable way would be to correlate situps with average speed ran over 40 yards.