Answer in Statistics and Probability for Waleed Abid #204963
The data set given below consists of six pairs of (x, y); (10, 70); (12, 65); (2, 96); (0, 94); (8, 75); (5, 82) I Based on a plot, determine whether the relationship between x and y is linear or not. a. b. Find the value of r to analyze the strength of the relationship.
a.
“defarraystretch{1.5}n begin{array}{c:c:c:c:c:c}n & x & y & xy & x^2 & y^2 \ hlinen & 10 & 70 & 700 & 100 & 4900 \n hdashlinen & 12 & 65 & 780 & 144 & 4225 \n hdashlinen & 2 & 96 & 192 & 4 & 9216 \n hdashlinen & 0 & 94 & 0 & 0 & 8836 \n hdashlinen& 8 & 75 & 600 & 64 & 5625 \n hdashlinen& 5 & 82 & 410 & 25 & 6724 \n hdashlinenSum=& 37 & 482 & 2682 & 337 & 39526 \n hdashlinenend{array}”
“bar{x}=dfrac{displaystylesum_{i=1}^nx_i}{n}=dfrac{37}{6}”
“bar{y}=dfrac{displaystylesum_{i=1}^ny_i}{n}=dfrac{482}{6}”
“SS_{xx}=displaystylesum_{i=1}^nx_i^2-dfrac{1}{n}big(displaystylesum_{i=1}^nx_ibig)^2=dfrac{653}{6}”
“SS_{yy}=displaystylesum_{i=1}^ny_i^2-dfrac{1}{n}big(displaystylesum_{i=1}^ny_ibig)^2=dfrac{4832}{6}”
“SS_{xy}=displaystylesum_{i=1}^ny_i^2-dfrac{1}{n}big(displaystylesum_{i=1}^nx_ibig)big(displaystylesum_{i=1}^ny_ibig)=-dfrac{1742}{6}”
“m=dfrac{SS_{xy}}{SS_{xx}}=-dfrac{1742}{653}approx-2.6677”
“n=bar{y}-mbar{x}=dfrac{482}{6}+dfrac{37}{6}cdotdfrac{1742}{653}approx96.7841”
“Y=96.7841-2.6667X”
The relationship between x and y is linear.
b.
“r=dfrac{SS_{xy}}{sqrt{SS_{xx}}sqrt{SS_{yy}}}=dfrac{-dfrac{1742}{6}}{sqrt{dfrac{653}{6}}sqrt{dfrac{4832}{6}}}approx-0.9807”
“r^2approx0.9617”
“0.7<rleq 1”
Strong negative correlation.
