Question

An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot.

Compute the least-squares line for predicting yield from pH. Round the answers to two decimal places.

pH	4.6	4.8	5.2	5.4	5.6	5.8	6
Yield	1056	1833	1629	1852	1783	2647	2171

Answer 1

The following data are passed:

pH	Yield
4.6	1056
4.8	1833
5.2	1629
5.4	1852
5.6	1783
5.8	2647
6	2171

The independent variable is pH, and the dependent variable is Yield. In order to compute the regression coefficients, the following table needs to be used:

	pH	Yield	pH*Yield	pH2	Yield2
	4.6	1056	4857.6	21.16	1115136
	4.8	1833	8798.4	23.04	3359889
	5.2	1629	8470.8	27.04	2653641
	5.4	1852	10000.8	29.16	3429904
	5.6	1783	9984.8	31.36	3179089
	5.8	2647	15352.6	33.64	7006609
	6	2171	13026	36	4713241
Sum =	37.4	12971	70491	201.4	25457509

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Yield = -2174.2754 + 753.7681 pH