Respuesta :
Answer:
a) r=-0.719
b) y=10.642-0.976x
c)Predicted y=7.714
Step-by-step explanation:
a)
sumx=1+4+6+7=18
sumy=9+7+8+1=25
sumxy=1*9+4*7+6*8+7*1=92
sumx²=1²+4²+6²+7²=102
sumy²=9²+7²+8²+1²=195
n=number of observation=4
The correlation coefficient is computed by following formula
[tex]r=\frac{nsumxy-(sumx)(sumy)}{\sqrt{[nsumx^{2} -(sumx)^2][nsumy^2-(sumy)^2]}}[/tex]
[tex]r=\frac{4(92)-(18)(25)}{\sqrt{[4(102) -(18)^2][4(195)-(25)^2]}}[/tex]
[tex]r=\frac{368-450}{\sqrt{[408 -324][780-625]}}[/tex]
[tex]r=\frac{-82}{\sqrt{[84][155]}}[/tex]
[tex]r=\frac{-82}{\sqrt{13020}}\\r=\frac{-82}{114.1052}\\r=-0.7186[/tex]
By rounding r to 3 decimal places we get r=-0.719.
b)
The regression equation can be written as y=a+bx
We have to find "a" and "b" for regression equation
[tex]b=\frac{nsumxy-(sumx)(sumy)}{{nsumx^{2} -(sumx)^2}}[/tex]
[tex]a=ybar-b(xbar)[/tex]
[tex]b=\frac{4(92)-(18)(25)}{{4(102) -(18)^2}}[/tex]
[tex]b=\frac{-82}{{84}}[/tex]
b=-0.976
xbar=sumx/n
xbar=18/4=4.5
ybar=sumy/n
ybar=25/4=6.25
a=ybar-b(xbar)
a=6.25-(-0.976)4.5
a=6.25+4.392
a=10.642
Thus, the regression equation is
y=a+bx
y=10.642-0.976x
c)
The predicted value of y for x=3 can be computed by putting the value of x in regression equation
y=10.642-0.976(3)
y=10.642-2.928
y=7.714
Hence, the predicted y-value for x=3 is 7.714.
