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Answer the following on regression and correlation.
Consider the data given below: Arithmetic mean 36 85 Standard deviation 11 8 and . Find the…
Consider the data given below:
and $r = 0.66$.
Find the regression coefficients.
| $x$ | $y$ | |
|---|---|---|
| Arithmetic mean | 36 | 85 |
| Standard deviation | 11 | 8 |
Answer
Answer
AIRegression coefficient of y on x: 0.48
Regression coefficient of x on y: 0.9075
Correlation coefficient r: 0.66
$b_{yx} = r\dfrac{\sigma_y}{\sigma_x} = 0.66 \times \dfrac{8}{11} = 0.48$
$b_{xy} = r\dfrac{\sigma_x}{\sigma_y} = 0.66 \times \dfrac{11}{8} = 0.9075$
From ISC 2025 Improvement Mathematics Paper 1, question 20(i).
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.