Question

b) Ten plots, each 10.4 meters, were randomly chosen in a large corm field. For each plot, the plant density (number of plants in the plot) and the mean cob weight (kg of grain per cob) were recorded. The results are given in the table below. Plant Density, X Cob Weight, Y 137 107 132 135 115 103 102 65 149 85 0.21 0.24 0.22 0.23 0.25 0.24 0.24 0.28 0.21 0.25 Calculate the linear regression of Yon X (9 marks)

Answer 1

Ans:

	X	Y	XY	X^2	Y^2
1	137	0.21	28.77	18769	0.0441
2	107	0.24	25.68	11449	0.0576
3	132	0.22	29.04	17424	0.0484
4	135	0.23	31.05	18225	0.0529
5	115	0.25	28.75	13225	0.0625
6	103	0.24	24.72	10609	0.0576
7	102	0.24	24.48	10404	0.0576
8	65	0.28	18.2	4225	0.0784
9	149	0.21	31.29	22201	0.0441
10	85	0.25	21.25	7225	0.0625
Total	1130	2.37	263.23	133756	0.5657

Slope,b=(10*263.23-1130*2.37)/(10*133756-1130^2)=-0.000755

y-intercept,a=(2.37-(-0.00076)*1130)/10=0.3223

Regression eqn:

Y'=-0.000755X+0.3223