Complete this question without the use of Minitab or Excel. PC Magazine provided
ID: 3225106 • Letter: C
Question
Complete this question without the use of Minitab or Excel.
PC Magazine provided ratings for several characteristics of computer monitors, including overall (PC Magazine website, April, 2015). The following data show rating for contrast ratio, resolution, and the overall rating for ten monitors tested using a 0-100 point scale. The highest rated monitor was the BenQ BL3201PH, with an overall rating of 87. a. Develop the estimated regression equation that can be used to predict the Overall Rating using the Contrast Ratio Rating. b. Develop the estimated regression equation that can be used to predict the Overall Rating using both the Contrast Ratio Rating and the Resolution Rating. c. Predict the overall Overall Rating for a computer monitor computer that has a Contrast Ratio Rating of 85 and a Resolution Rating of 74.Explanation / Answer
a)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
=10*57172-(695*817)/10*50601-(695*695)
=571720-567815/506010-483025
=3905/22985
=0.169893
b0=Ey-b1Ex/n
=817-0.169893*695/10
=817-694.83/10
=122.17/10
=12.217
y=b0+b1x
=12.217+0.169893x
b)
r (correlation(X1,Y))=n(Ex1y)-(Ex1)(Ey)/sqrt(nEx1^2-(Ex1)^2)(nEY^2-(Ey)^2)
=10(57172)-(695)(817)/sqrt(10*50601-(695)^2)(10*66869-(817)^2)
=571720-567815/sqrt(506010-483025)(668690-667489)
=3905/sqrt(22985)(1201)
=3905/5254.044
=0.74
Similarly,
r (correlation(X2,Y))=0.79647
r (correlation(X1,X2))=0.42
b1={ry,x1-ry,x2rx1,x2/1-(rx1,x2)^2}*{SDy/SDx1}
b1={0.74-0.79647*0.42/1-(0.42)^2}*{3.65/15.98}={0.4055/0.8236}*0.2284=0.4924*0.2284=0.11
b2={ry,x2-ry,x1*rx1,x2/1-(rx1,x2)^2}*{SDy/SDx2}
={0.79647-0.74*0.42/1-(0.42)^2}*{SDy/SDx2}
={0.48567/0.8236}*{3.65/5.62}
=0.38
a=y-b1x1-b2x2
=81.7-0.11*69.5-0.38*80.4
=81.7-7.645-30.552
=43.503
Hence, y =43.503+0.11x1+0.38x2
c)
y=43.503+0.11(85)+0.38(74)
=43.503+9.35+28.12
=80.973
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