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(i)

(ii)
Using the Graphing Calculator, $r = -0.99232 \approx -0.992$

The product moment correlation coefficient measures the strength and direction of a linear relationship between two variables. Thus, the r-value only indicate correlation, but not causality. It is possible for the relation to be non-linear, and yet have a value close to 1. We need to look at the scatter diagram to determine whether the relationship is truly linear.

(iii)
Using $y = a + bx^2, r = -0.99998$

Using $y = c + dx, r = -0.99232$

Since $|-0.99998|$ is close to 1. We conclude that $y = a + bx^2$ is the better model.

(iv)
Using Graphing Calculator, $y = 22.2 - 0.856x^2$

When $x = 3.2, y = 22.230 - 0.85621(3.2)^2 \approx 13.5$

Some students actually drew the scatter diagram for the given data, which was really strange. The meaning of r-value has to be well understood to answer (ii) well. Some actually don’t know what does least squares regression refer to.

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