All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Graph of 8i
Graph of 8i

(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

KS Comments:

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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