Question

Question 1. A soil management specialist was studying the relationship between the average temperature (in ºC) and the yield in bushels per acre for a certain crop. The data is given in Table 1 below.

Table 1

Region	Temperature		Yield
	(in ºC)		(in bushels per acre)
	X		Y
1	4		1
2	8		9
3	10		7
4	9		11
5	11		13
6	6		7

1. Construct a scatter a scatter diagram for the paired data.
2. As temperature increases, does yield appear to increase, decrease, or remain the same?
3. Compute the coefficient of correlation, and interpret it.
4. Compute the coefficient of determination and interpret it.

Answer 1

a. The scatter diagram for the paired data as follow. Temperature is plotted in X-axis and yield is plotted in Y-axis.

Scatter diagram for Temparature-Yield data 14 12 10 8 6 4. 12 10 6 A X t

b. From the diagram it is clear that, yield appears to increase as temperature increases.

Temperature Yield Region (in bushels (in eC) per acre) y- Y(X-X)(Y Y)2 (X - X)(Y - Y) a+bx (- 2 V 2.5881 29.28866161 4 -7 16 49 28 7 C 1 C 7.9997 0.00000009 3. 10 7 л 10.7055 7.31973025 4 1 11 1 9.3526 1.82952676 12.0584 16. 47061056 11 13 3 C 25 15 6 1 4 1 2 5.2939 7.32297721 47.9982 62.23150648 Total 48 48 4 36 46 Here n 6 48 = 8 X = 6 1 48 Yi = = 8 1 46 c. The coefficient of correlation is 1 1(x = x)?,/£ y- 34/86 =0.850685 The coefficient of correlation is positive and it is close to 1. So there is a strong positive correlation between X and Y. As temperature increases yield increases. d. Now we will find the regression line y on where = a + bx E(x- (y-y) b = 46 = 1.3529 34 a -bx= 8-1.3529 x 8 = -2,8235 and Therefore the regression line is = a + bx=-2.82351.3529x (-y2 62.2315 The coefficient of determiantion R2: =0.72 (yy 86 Therefore we can say 72% of the variance of y is explained by the correlation with x. 28% of y are unexplained part in this correlation.

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