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
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
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.