Question
[Maximum mark: 6]
Consider the following data
The regression line for y on x is y = 2.2x – 0.5
(a) Solve the equation above for x to find an expression in the form x = ay+b [2]
(b) Find the equation x = cy+d of the regression line for x on y. [2]
(c) Describe the advantage of the linear equation in (b). [2]
Answer/Explanation
Ans:
(a) y = 2.2x – 0.5 ⇔ y + 0.5 = 2.2x ⇔ x = 0.455 y + 0.227
(b) x = 0.423y + 0.385
(c) The relation in (a) is in fact the inverse function of the line y = 2.2x – 0.5
If y is given, the answer in (c) gives a more reliable estimation of x.
Question
[Maximum mark: 4]
Consider the following data
(a) Find Spearman’s rank correlation coefficient rs. [2]
(b) Describe the meaning of this coefficient. [2]
Answer/Explanation
Ans:
(a) rs = 1.
(b) It describes the monotonic relationship of the data. When x increases y also increases.
Question
[Maximum mark: 4]
Statements I, II, III, IV and V represent descriptions of the correlation between two variables.
I High positive linear correlation
II Low positive linear correlation
III No correlation
IV Low negative linear correlation
V High negative linear correlation
Which statement best represents the relationship between the two variables shown in each of the scatter diagrams below.
Answer/Explanation
Ans:
(a) II
(b) V
(c) III
(d) I