Question

Alex is a member of the school track and field team. His times for running various distances are shown. Create a scatter plot for the collected data. Label axes with the appropriate scales and titles. Draw a line of best fit. Predict the distance Alex can run in 20s. What type of correlation exists for the data? Give reasons. Distance (m) 50 100 150 200 250 Time 6.1 12 18.3 25.2 31.7

Answer 1

(1) Please find attached the graph of the data

(2) 160.396 m

(3) The correlation that exist is a straight line correlation

Explanation:

The given data are;

Distance, Time

(m), (s)

50, 6.1

100, 12

150, 18.3

200, 25.2

250, 31.7

(2)

Based on the linear regression formula, we have;

`b = (N\sum XY - \left (\sum X \right )\left (\sum Y \right ))/(N\sum X^(2) - \left (\sum X \right )^(2))`

`b = (5 * 17215 - 93.3 * 750)/(5 * 2156.03 -8704.89) = 7.758`

`a = (\sum Y - b\sum X)/(N)`

`a = (750 - 7.7581 * 93.3)/(5)= 5.234`

The line is

y = 7.7581×x+5.234

When t = 20 s, we have

y = 7.7581*20+5.234 = 160.396 m

(3) The correlation that exist is a straight line correlation