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 x overbarequals3.6667​, s Subscript xequals2.3381​, y overbarequals4.1000​, s Subscript yequals1.4588​, and requalsnegative 0.9265​, determine the​ least-squares regression line. ​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a). x 0 2 4 4 6 6 y 5.6 5.7 4.6 3.8 2.3 2.6 ​(a) Choose the correct graph below. A. 0 6 0 6 x y 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: (5.6,0), (5.8,2), (4.6,4), (3.8,4), (2.4,6), (2.6,6). All horizontal coordinates are approximate. B. 0 6 0 6 x y 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: (0,2.4), (2,2.6), (4,3.8), (4,4.6), (6,5.6), (6,5.8). All vertical coordinates are approximate. C. 0 6 0 6 x y 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: (0,0.4), (2,0.4), (4,1.4), (4,2.2), (6,3.8), (6,3.4). All vertical coordinates are approximate. D. 0 6 0 6 x y 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: (0,5.6), (2,5.8), (4,4.6), (4,3.8), (6,2.4), (6,2.6). All vertical coordinates are approximate. Your answer is correct. There appears to be a linear, negative relationship. ​(b) ModifyingAbove y with caretequals nothingxplusleft parenthesis nothing right parenthesis ​(Round to three decimal places as​ needed.)

Answer 1

(a)

Following is the scatter plot of the data,

Scatter plot shows a linear, negative relationship between the variables.

(b)

We have

Slope of the regression equation is

The Y intercept of equation is

Equation of regression line is

(c)

Following is the scatter plot with line: