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Sagot :
Solution
For this case we have the following data:
x y
0 996
1 923
2 882
3 892
4 840
5 813
sum xi = 15
sum yi = 5346
sum xi yi = 12788
sum xi^2 = 55
And we want to find and equation like this one:
y= mx+ b
So then we can estimate the slope using least squares and we have:
[tex]m=\frac{n\sum ^n_{i=1}x_iy_i-\sum ^n_{i=1}x_i\sum ^n_{i=1}y_i}{n(\sum ^n_{i=1}x^2_i)-(\sum ^n_{i=1}x_i)^2}[/tex]Replacing we have:
[tex]m=\frac{6\cdot12788-(15\cdot5346)}{6(55)-(15)^2}=\frac{-3462}{105}=-32.971[/tex]m= -32.971
And the intercept would be:
[tex]b=\frac{\sum^n_{i=1}y_i}{n}-m\cdot\frac{\sum^n_{i=1}x_i}{n}=\frac{5346}{6}-(-32.971)\cdot\frac{15}{6}=973.429[/tex]b= 973.428
Then the equation would be:
y= -32.971x+ 973.428
And we can find the value of x for y = 767 and we got::
767 = -32.971x+ 973.428
Solcing for x we have:
767- 973.428 = -32.971 x
x= 6.26
Regression Equation: y= -32.9x + 973.4
Final Answer: 2012
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