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Answer the following on regression and correlation.
By using the data , , and , find: The regression equation on . What is the most likely value of…
By using the data $\bar{x} = 25$, $\bar{y} = 30$, $b_{yx} = 1.6$ and $b_{xy} = 0.4$, find:
(a)[1.0]
The regression equation $y$ on $x$.
(b)[1.0]
What is the most likely value of $y$ when $x = 60$?
(c)[1.0]
What is the coefficient of correlation between $x$ and $y$?
Answer
Answer (a)
AILine of y on x: y = 1.6x - 10
$y - \bar{y} = b_{yx}(x - \bar{x})$
$y - 30 = 1.6(x - 25)$
Hence $y = 1.6x - 10$.
Answer (b)
AIAt $x = 60$: $y = 1.6(60) - 10 = 86$.
Hence the most likely value of $y$ is $86$.
Final answer: $86$
Answer (c)
AI$r^2 = b_{yx}\cdot b_{xy} = 1.6 \times 0.4 = 0.64$
Both coefficients are positive, so $r > 0$.
Hence $r = 0.8$.
Final answer: $0.8$
From ISC 2017 Mathematics Paper 1, question 1(vii).
Check your working with the Regression lines calculator: both regression lines, b_yx, b_xy and r from data, summary sums or the two lines; with estimates.