Answer in Statistics and Probability for bebeya #248593
find the regression analysis, what is the value of a,b, and what is expected y if x=18
X: 17 12 10 20
Y: 10 10 8 12
“bar{X}=dfrac{1}{n}displaystylesum_{i=1}^nX_i=dfrac{59}{4}=14.75”
“bar{Y}=dfrac{1}{n}displaystylesum_{i=1}^nY_i=dfrac{40}{4}=10”
“SS_{XX}=displaystylesum_{i=1}^nX_i^2-dfrac{1}{n}(displaystylesum_{i=1}^nX_i)^2”
“=933-dfrac{(59)^2}{4}=62.75”
“SS_{YY}=displaystylesum_{i=1}^nY_i^2-dfrac{1}{n}(displaystylesum_{i=1}^nY_i)^2”
“=408-dfrac{(40)^2}{4}=8”
“SS_{XY}=displaystylesum_{i=1}^nX_iY_i-dfrac{1}{n}(displaystylesum_{i=1}^nX_i)(displaystylesum_{i=1}^nY_i)”
“=610-dfrac{59(40)}{4}=20”
The regression coefficients (the slope “m,” and the y-intercept “n”) are obtained as follows:
“m=dfrac{SS_{XY}}{SS_{XX}}=dfrac{20}{62.75}=0.318725”
“n=bar{Y}-mbar{X}=10-dfrac{20}{62.75}(14.75)=5.298805”
We find that the regression equation is:
“Y=5.298805+0.318725X”
Correlation coefficient
“r=dfrac{SS_{XY}}{sqrt{SS_{XX}}sqrt{SS_{YY}}}=dfrac{20}{sqrt{62.75}sqrt{8}}=0.892644”
Strong positive correlation.
“r^2=dfrac{(20)^2}{62.75(8)}=0.796813”
“Y(18)=5.298805+0.318725(18)=11.035855”
