A study into the germination of parsnip seeds in the 1980s produced the following data for the average $C$ number of days, $d$, taken for a seed to germinate at different soil temperatures, $t$, measured in degrees Fahrenheit.

(i) Sketch a scatter diagram of the data. State the product moment correlation coefficient between $d$ and $t$

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(ii) Lim thinks the data can be modelled by the regression equation $d=-a+b u$, where $u=\frac{1}{t}$. Find the values of $a$ and $b$ for Lim’s model, giving the values correct to 3 significant figures. State the product moment correlation coefficient between $d$ and $u$.

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The study also found that, at a soil temperature of 86 degrees Fahrenheit, parsnip seeds took an average of 32 days to germinate.

(iii) Determine whether Lim’s model fits this additional data.

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A temperature of $F$ degrees Fahrenheit is equivalent to a temperature of $C$ degrees Celsius, where $C=\frac{5}{9}(F-32)$

(iv) Write Lim’s equation from part (ii) in terms of $d$ and $T$, where $T$ is the temperature in degrees Celsius.

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