Question

use the data set to the right to answer the following questions
a. sketch a scatter - plot
b. if one pair of (x,y) values is removed, the correlation for the remaining four pairs equals 1. which pair is it?
(4,2) (type an ordered pair)
c. if one y - value is changed, the correlation for the five pairs equals 1. identify the y - value and how it must be changed for this to happen
the y - value of would have to change to

Explanation:

Step1: Analyze scatter - plot points

The data set has points \((x,y)\) as \((2,9)\), \((3,12)\), \((4,2)\), \((5,18)\).

Step2: For part b

A correlation of 1 means a perfect positive - linear relationship. By observing the points, the point \((4,2)\) is an out - lier. Removing it may give a perfect positive linear relationship for the remaining points.

Step3: For part c

Let the points be \((x_1,y_1)=(2,9)\), \((x_2,y_2)=(3,12)\), \((x_3,y_3)=(4,2)\), \((x_4,y_4)=(5,18)\). For a perfect positive linear relationship \(y = ax + b\). First, find the slope between two non - outlier points, say \((2,9)\) and \((3,12)\). The slope \(a=\frac{12 - 9}{3 - 2}=3\). Using the point - slope form \(y - y_1=a(x - x_1)\) with \((x_1,y_1)=(2,9)\) and \(a = 3\), we have \(y-9 = 3(x - 2)\) or \(y=3x+3\). When \(x = 4\), \(y=3\times4 + 3=15\). So the \(y\) value of \(2\) (corresponding to \(x = 4\)) should be changed to \(15\).

Answer:

b. \((4,2)\)
c. The \(y\) value of \(2\) would have to change to \(15\)