Question

A data set is given below. ​(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ​(b) Given that x̅ = 3.8333​, Sx = 2.4014 ​, ȳ equals = 3.7333 3.​, Sy = 1.8381​, and r = -0.9545 ​, determine the​ least-squares regression line.

(c) Graph the​ least-squares regression line on the scatter diagram drawn in part

x   y
0   5.9
2   5.7
4   4.3
5   2.8
6   1.7
6   2

​(a) Choose the correct graph below.

A.

• A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,6), (2,5.8), (4,4.4), (5,2.8), (6,1.8), (6,2). All vertical coordinates are approximate. Your answer is correct.

There appears to be

a linear, negative

relationship.

​(b)ŷ __?__x+( __?__)

​(Round to three decimal places as​ needed.)

​

(a).

Answer 1

A) The following scatter plot is obtained based on the data provided:

There appears to be a negative linear relationship.

B)

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

	X	Y	X*Y	X2	Y2
	0	5.9	0	0	34.81
	2	5.7	11.4	4	32.49
	4	4.3	17.2	16	18.49
	5	2.8	14	25	7.84
	6	1.7	10.2	36	2.89
	6	2	12	36	4
Sum =	23	22.4	64.8	117	100.52

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:

Y = 6.5341 - 0.7306 * X

Graphically:

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