Bivariate Data, SM-Bank 015

The heights (in cm) and ages (in months) of a random sample of 15 boys have been plotted in the scatterplot below.

A line of best fit has been fitted to the data.

State the independent variable in the graph. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Describe this association in terms of strength and direction. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
Determine the gradient of the line of best fit, giving your answer correct to one decimal place. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

i. \(\text{Independent variable: age (months)}\)

ii. \(\text{Association: strong and positive}\)

iii. \(0.5\)

Show Worked Solution

i. \(\text{Independent variable}\ \ \Rightarrow\ \ x\text{-axis variable} \)

\(\text{age (months)}\)

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

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

\(\text{Direction: positive (as age ↑, height ↑)}\)

iii. \(\text{LOBF passes through (15, 83.25) and (35, 94)} \)

\(\text{Gradient}\ = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{94-83.25}{35-15} = 0.5375 = 0.5\ \text{(1 d.p.)} \)