Question

Crops growth depends on many factors (temperature, humidity etc.). One of them is soil acidity. The table below shows the crop and soil pH in 7 plots side by side (all of the other growing conditions are identical except the pH)

Soil pH 4.6 4.8 5.2 5.4 5.6 5.8 6 Crop [lb/acre]

1056 1833 1629 1852 1783 2647 2131

5.1 (6%)

Calculate the correlation coefficient between the crop and pH, assuming there is a linear correlation between the two of them.

5.2 (7%)

Calculate the least-squares line (the crop as a function of pH). Round the answers to two decimal places.

5.3 (7%)

If a new plot, with the pH=7 is planted, can you use the least square computed above to predict the crop?

A) Yes: explain why and predict the yield

B) No: explain why not

Answer 1

5.1

PH(X)	crop(Y)
4.6	1056
4.8	1833
5.2	1629
5.4	1852
5.6	1783
5.8	2647
6	2131

The formula for Corelation coefficient between ph and crop is as follows=

By calculating above variables with given data,

we get correlation coefficient(r) as 0.7829.

5.2

The least square line between the Crop(Y) and PH(X) can be calculated by using:

ŷ=b₁x+b₀

By passing the given data in the above equation ,

we get Least square line as ŷ=737.10x-2090.94

5.3

When PH value is changed to 7,we cannot predict the least square line because their is no relationship exists between crop and PH. For any crop the PH remains same i.e,There is no effect on changing PH.