Question

Five observations taken for two variables follow. | 4 yi | 50 6 50 11 40 3 60 16 | 30 a. Which of the following scatter diagrams accurately represents the data set? A. - B. . 60 ----- 50 ------- 운 요 요 10. 20 30 .. ... 19. 20. ..30 ..

Answer 1

a) The accurate scatter-plot for the given data set is plotted as:

C)

10 去

b) Based on the scatter-plot developed in part a, we can see that there is a strong relationship between the two variables but there is a negative relationship.

The relationship appears to be negative and strong because the line that is generating due to the dots is an almost straight line and the slope is downwards.

So, there is a strong and negative relationship

c) The following table calculation is used to find the sample covariance as:

X;.Y 200 300 440 180 480 Sum = 1600

The sum of squares is calculated as:

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= 1600 3 9200 = -240

Now the covariance is calculated as:

COU(X,Y) = SSXY n-1 -240 5-1 = -60

d) To calculate the correlation coefficient we need to calculate the following table as:

X*Y y2 200 2500 300 2500 440 1600 180 3600 480 900 Sum = 1600 11100

The sum of squares are calculated as:

(43)(*3)*-**3= 185 (= AXSS

5ι: - Σ ! (Σκ) 55, Σr (Σ) SSyY =Σ.

Based on the data provided the sum of squares are calculated as:

SSxy = 1600 - 3 (40 x 230) = –240 55xx = 438 – }(20) = 118 SSyy = 11100 – (230)2 = 520

Now the correlation is calculated as:

r= SSXY SSxx SSyy -240 118 x 520 = -0.969

Based on the sample correlation coefficient we can conclude that:

There is a strong negative linear relationship.

Because the correlation close to 1 or -1 is said to have a strong.