Question

Given the ordered pairs (4, 39), (6, 36), (8, 33), and (10, 30), complete the following.

(a) Find the coefficient of linear correlation. Interpret the coefficient of linear correlation.

There is no linear correlation.

There is a weak linear correlation.

There is a strong linear correlation.

(b) Find the line of best fit. ŷ = x +

Answer 1

a) For the given ordered pairs (4, 39), (6, 36), (8, 33), and (10, 30) to calculate the linear correlation we need to do teh following table calculation as:

The mean of X and Y variable are calculated as:

Now the sum of squares is calculated as:

Now the correlation is calculated as:

Now from the correlation calculation we can see that it is -1 which is an absolute negative correlation.

Thus There is a strong linear correlation.

b) Now the regression equation is computed as:

Y = m*X + n

Where the slope m is calculated as:

and the intercept n is calculated as:

Thus the regression equation is computed as:

Y=−1.5X + 45