An agricultural researcher is investigating the relationship between the soil moisture content, mmm as a percentage, and the final crop yield, yyy in tonnes per hectare, across 8 test plots. The experimental results are summarized in the table below.
| Plot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Moisture mmm (%) | 15.2 | 16.8 | 18.5 | 20.4 | 21.6 | 23.2 | 25.1 | 26.8 |
| Yield yyy (tonnes) | 29.5 | 32.0 | 35.0 | 39.5 | 41.0 | 44.5 | 47.5 | 51.0 |
You may use: Smm=113.5S_{mm} = 113.5Smm=113.5 Smy=212.4S_{my} = 212.4Smy=212.4 Syy=398.0S_{yy} = 398.0Syy=398.0 ∑m=167.6\sum m = 167.6∑m=167.6 ∑y=320.0\sum y = 320.0∑y=320.0
Find the product moment correlation coefficient between yyy and mmm.
Give a reason why a linear regression model of the form y=a+bmy = a + bmy=a+bm is appropriate for these data.
Find the value of bbb correct to 3 decimal places.
Find the equation of the regression line of yyy on mmm.
Interpret your value of bbb in context.
Use your answer to part (d) to estimate the crop yield when the soil moisture content is 22.0%22.0\%22.0%.
Comment on the reliability of your estimate in part (f), giving a reason.
