# Simple linear regression - understanding given

The question is to fill out the missing numbers (A-L) of a simple linear regression model. I am having problems with converting and interpreting the given table in terms of variables. Would it be possible for someone to confirm and clarify things for me.

The first table represents regression statistics

True model $$Y_t = \beta_o + \beta_1X_t + \mu_t$$

Estimated model $$\hat Y_t = \hat\beta_0 + \hat\beta_1x_t$$

This is what I am confused about

• Does the first standard error (12.8478) mean $\sum\hat\mu_t^2$ ?
• Does the standard error for the intercept in last table (14.6208) mean $\sum\mu_t^2$ ?
• Does 3.8508 equal $\hat\beta_1$ ?
• In order to calculate RSS (for J) I need $\sum \hat\mu_t^2$ does this confirm that my first two points are incorrect
• I know $G=\hat\beta_1^2\sum x_t^2$, how do I find $\sum x_t^2$

If I am wrong, would it be possible to know what those numbers mean in terms of variables

1. The standard error here refers to the standard error of the model as a whole, and it is the standard deviation divided by the square root of the sample size.

2. Here the standard error refers to the individual standard error for the intercept. The formula is same as that in the first point.

(To get the answer for K and L; use this -> T stat = Coefficient / Std .Error)

3. Yes its the estimated coefficient of X variable 1

For the rest of the confusion, watch this youtube video!

EDIT:

I used some identities to figure out G H I J, so i cant guarantee this is what your lecturer wants.

Calculating D, E, F:

these are the degrees of freedom, some formulas here, D -> 1 E -> 13 F -> 14

Calculating H, G:

1. F statistic(=24.15) = I / J.
2. I is G/D; similarly J is H/E
3. You know D and E so just some math will get you the value for G and H.

This is a really weird approach, but I don't think you can get the sum of squares for regression and residual without the actual observations.

• thanks! that helps a lot. any clues on figuring out G? – Kartik Oct 29 '13 at 6:30
• hey look at the edit kartik – Siddharth Gopi Oct 29 '13 at 7:07