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


Graph of 8i
Graph of 8i

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.

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.

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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