Question

Altitude,_x   Speed_of_sound,_y
0   1115.6
5   1095.9
10   1077.6
15   1055.8
20   1036.6
25   1014.9
30   994.1
35   968.2
40   966.2
45   966.2
50   966.2

For the following data​ (a) display the data in a scatter​ plot, (b) calculate the sample correlation coefficient​ r, and​ (c) make a conclusion about the type of correlation. Use technology.

The altitudes​ (in thousands of​ feet) and speeds of sound​ (in feet per​ second) at these altitudes are shown in the data set below.

Answer 1

(a) SCATTER PLOT:

I have used excel to construct scatter plot for the given data.

From the scatter plot, the data show a downhill linear pattern as we move from left to right, this indicates a negative linear relationship between Altitude (x) and Speed of sound (y). Thus as the value of Altitude (x) increase (move right) the value of Speed of sound (y) tend to decrease (move down).

(b) SAMPLE CORRELATION COEFFICIENT:

I have used R code to calculate sample correlation coefficient (r).

Thus the sample correlation coefficient (r) is .

(c) CONCLUSION:

Since the sample correlation coefficient is negative and closer to , there is a strong negative linear correlation between Altitude (x) and Speed of sound (y).