Question

8. If the data set shown below were used to fit the following simple regression model, y = Bo + Bix te, which of the followin

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Answer #1

Solution:

The correct answer is d) All of the above

Explanation:

Let's first consider the equation:

y=2x

The predicted values of y are:

\hat{y}_{1}=2 \times 2=4

\hat{y}_{2}=2 \times 2=4

\hat{y}_{3}=2 \times 2=4

\therefore SSE=\sum (y_{i}-\hat{y}_{i})^{2}

  =(3-4)^{2}+(4-4)^{2}+(5-4)^{2}

=1+0+1

=2

Now let's consider the second option:

y=2+x

The predicted values of y are:

\hat{y}_{1}=2 +2=4

\hat{y}_{2}=2 + 2=4

\hat{y}_{3}=2 + 2=4

\therefore SSE=\sum (y_{i}-\hat{y}_{i})^{2}

  =(3-4)^{2}+(4-4)^{2}+(5-4)^{2}

=1+0+1

=2

Now let's consider the third option:

y=3+0.5x

The predicted values of y are:

\hat{y}_{1}=3 +0.5 \times 2=4

\hat{y}_{2}=3+ 0.5 \times 2=4

\hat{y}_{3}=3 +0.5 \times 2=4

\therefore SSE=\sum (y_{i}-\hat{y}_{i})^{2}

  =(3-4)^{2}+(4-4)^{2}+(5-4)^{2}

=1+0+1

=2

Since all the equations have same SSE, therefore, the option d) All of the above is correct

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