Analysis and Approaches for IBDP Maths Ebook 1 | Page 307

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3. The following table below shows the age x of a person and the score y on a memory
test of five patients.
Age ( x ) 62 65 69 72 80
Score ( y ) 7.7 6.5 8.2 8.1 7.1
Let L
1
be the regression line of y on x . The equation of the line L
1
can be written in the
form y �ax � b , and the corresponding correlation coefficient is r 1
.
(a) Find the values of a and b .
[2]
Let L
2
be the regression line of x on y . The equation of the line L
2
can be written in the
form x �cy � d ,and the corresponding correlation coefficient is r 2
.
r2
(b) Write down the value of
r . 1
[1]
(c) Find the x -intercept of L
2
.
[2]
4. The following table shows the Art exam score x and the Music exam score y for six
students.
Art exam score ( x ) 80 77 52 68 82 43
Music exam score ( y ) 97 85 65 77 92 93
Let L
1
be the regression line of y on x . The equation of the line L
1
can be written in the
form y �ax � b , and the corresponding correlation coefficient is r 1
.
(a) Find the values of a and b .
[2]
Let L
2
be the regression line of x on y . The equation of the line L
2
can be written in the
form x �cy � d ,and the corresponding correlation coefficient is r 2
.
22
(b)
Write down the value of
r
1
r . 2
[1]
(c) Find the x -coordinate of the point of intersection of L
1
and L
2
.
[2]
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