California highways were monitored and the following relationship between speed and breaking distance was observed. Speed (mph) Distance (ft) 30 50 40 81 50 125 60 186 70 246 80 318 (a) Find the linear correlation coefficient between the two variables. (b) Is the relation between speed and distance linear?
California highways were monitored and the following relationship between speed and breaking distance was observed.
| Speed (mph) | Distance (ft) |
| 30 | 50 |
| 40 | 81 |
| 50 | 125 |
| 60 | 186 |
| 70 | 246 |
| 80 | 318 |
(a) Find the linear
(b) Is the relation between speed and distance linear?
a)
Enter the data in the cells A1:B6.
The correlation coefficient using the Excel formula “=CORREL (A1:A6, B1: B6)” is
0.9914.
b)
Testing
The hypotheses are given below:
Null hypothesis:
H0: ρ= 0
Alternative hypothesis:
Ha: ρ ≠ 0.
Degrees of freedom:
The formula for degrees of freedom is as follows:
Df = n – 2.
The number of data values given are 6, that is n = 6.
Substitute n = 6 in the degrees of freedom formula.
Df = n – 2 = 6 – 2 = 4.
Assume the level of significance for the test is 0.05.
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