Question

The regression line y = 3 + 2x has been fitted to the data points (4,8), (2,5) and (1,2). the sum of squared residuals will be:

Answer 1

(8 3
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Answer 2

Answer:

The sum of squared residual terms will be 22.

Step-by-step explanation:

Correction in question :

The regression line will be given as -

$\hat{y} = 3 +2x$

Solution -

Given the first data, the point is (4,8) -

From here we can write -

y = 8

x = 4

$\hat{y} = 3+2x = 3+2\times4 = 3+8=11$

Now, the residual $e_i$ is given by -

$e_i = y - \hat{y} = 8-11 = -3$

Now squared residual will be -

$e^2_i = 9$

Given the second data, the point is (2,5) -

From here we can write -

y = 5

x = 2

$\hat{y} = 3+2x = 3+2\times2 = 3+4=7$

Now, the residual $e_i$ is given by -

$e_i = y - \hat{y} = 5-7 = -2$

Now squared residual will be -

$e^2_i = 4$

Given the third data, the point is (1,2) -

From here we can write -

y = 2

x = 1

$\hat{y} = 3+2x = 3+2\times1 = 3+2=5$

Now, the residual $e_i$ is given by -

$e_i = y - \hat{y} = 2-5 = -3$

Now squared residual will be -

$e^2_i = 9$

The sum of squared residual will be = $9+4+9$ = 22

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