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Login NowThe properties of corelation cofficient are:

- Correlation cofficient liea between -1 to +1
i.e. -1 ≤ x ≤ +1
- Correlation cofficient is symmetrical
i.e. r
_{xy}= r_{yx}= r - Correlation cofficient is independent of change of origin and scale.
- Correlation cofficient is the geometric mean of the two regression cofficient \(r = \pm \sqrt{b_{yx} \times b_{xy}}\)
- Correlation cofficient has no unit because of relative measure.

**Solution:**

In the given problem we have two variables: the transmission time and average size of file.

Y = transmission time

X = average file size

The linear regression model is given by

Y = a + bX

The slope b is given by

b = correlation coefficient × \(\frac{SD_{y}}{SD_{x}}\)

Where SD_{y} is the standard deviation of average transmittance time and SD_{x} is the standard deviation of average file size.

b = \(0.86 \times \frac{0.01}{35}\)

b = 0.0002457

The y-intercept a is given by

a = y – bx

a = 0.04 – (0.0002457) × 126

a = 0.04 – 0.030958

a = 0.009042

Therefore, the linear regression model is

**Y = 0.009042 + 0.0002457X**

**Part II:**

Predict the time it will take to transmit a 400 Kbyte file.

Substitute X = 400 in the regression model

Y = 0.009042 + 0.0002457 × (400)

Y = 0.009042 + 0.09828

**Y = 0.1073 seconds**

Therefore, the predicted time to transmit a 400 Kbyte file is 0.1073 seconds.

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