Question

The scatter diagram for the data set below is shown. ​(a) Given that x overbar equals 2.5 commax=2.5,s Subscript x Baseline equals 2.258318 commasx=2.258318,y overbar equals 4.083 commay=4.083,s Subscript y Baseline equals 2.1046773 commasy=2.1046773,and r equals negative 0.9530761 commar=−0.9530761,determine the​ least-squares regression line. ​(b) Graph the​ least-squares regression line on the scatter diagram. -16-38xy A scatter diagram has a horizontal x-axis labeled from negative 1 to 6 in increments of 1 and a vertical y-axis labeled from negative 3 to 8 in increments of 1. The following 6 points are plotted, listed here from left to right: (0, 7); (0, 5.6); (2, 4.9); (3, 3.1); (5, 2.5); (5, 1.4). The points follow the general pattern of a line that falls from left to right. x 00 00 22 33 55 55 y 77 5.65.6 4.94.9 3.13.1 2.52.5 1.41.4

Answer 1

Solution:

Given:

$\bar{x}=2.5\: \: \: \: ,S_{x}=2.258318$

$\bar{y}=4.083\: \: \: \: ,S_{y}=2.1046773$

r = -0.9530761

Part a) Find the equation of least squares regression line.

$y = b_{0}+ b_{1} \times x$

where

$b_{1} = r \times \frac{S_{y}}{S_{x}}$

$b_{1} = -0.9530761 \times \frac{2.1046773}{2.258318}$

$b_{1} = -0.88824$

and

$b_{0} =\bar{y}-b_{1} \times \bar{x}$

$b_{0} =4.083-(-0.88824) \times 2.5$

$b_{0} =4.083 + 2.22059$

$b_{0} =6.30359$

$b_{0} =6.304$

Thus least-square regression line is:

$y = b_{0}+ b_{1} \times x$

$y = 6.304 - 0.88824 \times x$

Part b) Graph the​ least-squares regression line on the scatter diagram.