In: Statistics and Probability
The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days.
Day | Time | Heart Rate |
1 | 35.53 | 151 |
2 | 34.47 | 148 |
3 | 34.96 | 126 |
4 | 34.45 | 151 |
5 | 35.16 | 140 |
6 | 36 | 149 |
7 | 34.44 | 135 |
8 | 35.41 | 155 |
9 | 34.06 | 128 |
10 | 35.5 | 125 |
For computation purposes,
?¯x¯ = 34.998 , ?¯y¯ = 140.8 , ∑?∑x= 349.98 , ∑?∑y = 1408 , ∑??∑xy
= 49295.03 , ∑?2∑x2 = 12252.1068 , ∑?2∑y2 = 199442 ,
Use swim time as the explanatory variable ?x and compute the
correlation coefficient, then find the least-squares regression
line.
The correlation coefficient is ?=r= . (Round to 4 decimal places.)
The equation of the least squares line is
?̂ =y^= + x. (Round to 4 decimal places.)