MultiLinear regression analysis - have answer just need someone to verify

Can you please help me with the following question.

I have obtained the following values of

\begin{bmatrix} \beta_0 \\ \beta_1 \end{bmatrix}= \begin{bmatrix} 8.04 \\ 0.62 \end{bmatrix}

for b i)

multilinear regression.PNG40.2KB

Reply 1

ghostwalker

17

Original post by ajayhp

Can you please help me with the following question.

I have obtained the following values of

\begin{bmatrix} \beta_0 \\ \beta_1 \end{bmatrix}= \begin{bmatrix} 8.04 \\ 0.62 \end{bmatrix}

for b i)

Just ran the data through LINEST on Excel, and I get 7.977777778 0.546153846 respectively for the two parameters.

Assuming it's the standard least squares regression, we appear to have a discrepancy.

Reply 2

ajayhp

OP

3

Original post by ghostwalker

Just ran the data through LINEST on Excel, and I get 7.977777778 0.546153846 respectively for the two parameters.

Assuming it's the standard least squares regression, we appear to have a discrepancy.

Hi ghostwalker.

I have also run it in SAS and it appears to give your answer.

How would i go about answering the question then? Any Ideas?

Thanks for your reply btw.

Reply 3

ghostwalker

17

Original post by ajayhp

Hi ghostwalker.

I have also run it in SAS and it appears to give your answer.

How would i go about answering the question then? Any Ideas?

Thanks for your reply btw.

I'm not well up on the theory, and have no idea what an X matrix is in the context, nor how you got the values you posted, or what part a) of the question was.

If you can elaborate I may be able to help, but can't guarantee it.

Reply 4

ajayhp

OP

3

For a generalised Linear model:

[latex/]Y = X\hat{\beta} + e_{ij}

Where
[latex/]\hat{\beta}=\begin{bmatrix} \hat{\beta_0} \\\hat{\beta_1} \end{bmatrix}

The X matrix is as folows:

[latex/] \begin{bmatrix} 1 & -2 \\ 1 & -1 \\ 1 & 0 \\ 1 & 1 \\ 1 & 2 \end{bmatrix}

We also have:

[latex/] \hat{\beta} = (X^{T}X)^{-1} X^{T}y

what would Y be in this case

Original post by ghostwalker

I'm not well up on the theory, and have no idea what an X matrix is in the context, nor how you got the values you posted, or what part a) of the question was.

If you can elaborate I may be able to help, but can't guarantee it.

Reply 5

ajayhp

OP

3

Since Y has some repeated values maybe i can remake the whole of the matrix X

[latex/] X = \begin{bmatrix} 1 & -2 \\ 1 & -2 \\ 1 & -2 \\ 1 & -1 \\ 1 & -1 \\ 1 & -1 \\ 1 & 0 \\ 1 & 0 \\ 1 & 0 \\ 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & -2 \\ 1 & -2 \\ 1 & -2 \end{bmatrix}

so then Y would be:

[latex/] Y = \begin{bmatrix} 6.9 \\ 6.6 \\ 7.2 \\ 7.1 \\ 0 \\ 0 \\ 8.3 \\ 0 \\ 0 \\ 8.7 \\ 0 \\ 0 \\ 9.2 \\ 8.5 \\ 9.3 \end{bmatrix}

(edited 10 years ago)

Reply 6

ghostwalker

17

Original post by ajayhp

...

I'm guessing there, and can't find anything in the literature available to me.

But since y is actually the Y matrix of values, I suspect you need to have all 9 values in the Y matrix, and add repeats to the X matrix as necessary.

As per your last post, but without the zero entries, so 9 columns in each.

But I am guessing!

MultiLinear regression analysis - have answer just need someone to verify

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