Bivariate Data, SM-Bank 014

The scatterplot below displays the mean age, in years, and the mean height, in centimetres, of 648 women from seven different age groups.

In an initial analysis of the data, a line of best fit is drawn, as shown.

Describe this association in terms of strength and direction. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
Determine the mean height predicted for a group of 65 year old women. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

i. \(\text{Association: strong and negative}\)

ii. \(\text{Predicted height = 160.5 cm}\)

Show Worked Solution

i. \(\text{Association:} \)

\(\text{Strength: strong (data points are tightly gathered to the LOBF)}\)

\(\text{Direction: negative (as mean age ↑, mean height ↓)}\)

ii. \(\text{Mean age = 65}\ \ \Rightarrow \ \ \text{Predicted height = 160.5 cm}\)