A sample of 80 women is obtained, and their heights (in inches) and pulse rates
ID: 3223400 • Letter: A
Question
A sample of 80 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.242 and the equation of the regression line is ModifyingAbove y=17.7+0.930x, where x represents height. The mean of the 80 heights is 63.4 in and the mean of the 80 pulse rates is 73.3 beats per minute. Find the best predicted pulse rate of a woman who is 74 in tall. Use a significance level of alpha =0.05.
(Please Ref critical values of the pearson correlation coefficient r)
n
=0.05
=0.01
4
0.950
0.990
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.590
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.430
n
=0.05
=0.01
4
0.950
0.990
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.590
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.430
Explanation / Answer
Give value of correlation is 0.242 which is not high means there is not high linear correlation between height and pulse rate. This means it is less likely to see increase in the pulse rate with unit increase in the height.
Further to find out the best predicted value of pulse rate when height is 74, substitute value of x= 74 in the regression euqation. After solving this equation we get predicted value as 70.5.