Question

a data set is given.
(a) draw a scatter diagram. comment on the type of relation that appears to exist between x and y.
(b) given that ( overline{x}=3.8333, s_{x}=2.1370, overline{y}=4.0000, s_{y}=1.6840 ), and ( r=-0.9337 ), determine the least-squares regression line.
(c) graph the least-squares regression line on the scatter diagram drawn in part (a).

(a) choose the correct graph.

Explanation:

Step1: Calculate the slope \(b_1\)

The formula for the slope of the least - squares regression line is \(b_1=r\frac{s_y}{s_x}\).
Given \(r = - 0.9337\), \(s_y=1.6840\), \(s_x = 2.1370\)
\(b_1=-0.9337\times\frac{1.6840}{2.1370}\)
\(b_1=-0.9337\times0.788\approx - 0.736\)

Step2: Calculate the intercept \(b_0\)

The formula for the intercept is \(b_0=\bar{y}-b_1\bar{x}\)
Given \(\bar{x}=3.8333\), \(\bar{y}=4.0000\), \(b_1=-0.736\)
\(b_0 = 4-(-0.736)\times3.8333\)
\(b_0=4 + 2.822\approx6.822\)

Answer:

The least - squares regression line is \(\hat{y}=-0.736x + 6.822\)