Question

Question 7 (Unit 9) 10 marks Figure 2 shows a scatterplot of r and y values for each of 100 data points in a sample 2 2 3 X Figure 2 The correlation coefficient associated with Figure 2 is claimed to be -0.9. (a) Is the value claimed for the correlation coefficient plausible in terms of its sign? Justify your answer [2] (b) Is the value claimed for the correlation coefficient plausible in terms of its closeness to -1? Justify your answer [2] In parts (c), (d) and (e), further statements are made about the relationship between and y in Figure 2. In each case, state whether or not the statement is correct, giving a reason for your answer (c) If each value of the y variable is doubled, then the value of the 2] correlation coefficient will be halved. (d) If the values of x and y are swapped over, then this will change the sign of the correlation coefficient 2] (e) Figure 2 shows that the variable x causes the variable y to take the values that it does 2]

Answer 1

a) Yes. We can see that the value of decreases as the value of increases. So there is an inverse relationship between . So the sign of the correlation is negative.

b) Yes. We can see that the values of x and y aligns almost in a straight line. A perfect straight line will have correlation .

+1

Since the sign is negative and the values are almost in a straight line, the claimed value is plausible.

0.9

c) The correlation coefficient is calculated as

ΤΣΧΥ-ΣΧΣΥ νηΣΧ Σx nΣΥ ΣΥ2

False.

When the value of is doubled,
ΣΧΥΣΥ xy,
are doubled and
y)a
are quadrupled.

Thus,

2n Σxy-2ΣΧΣΥ ΣΧΣX -4nΣy4ΣΥΣ νηΣ

The correlation coefficient is the same.

d) False. We see if you interchange x and y, the formula remains the same.

ΤΣΧΥ-ΣΧΣΥ νηΣΧ Σx nΣΥ ΣΥ2

e) Yes. The value of y is dependent on x.