A.     What is the least squares estimator of á?

B.     What is the least squares estimator of â₁, the coefficient of X₁?

C.    What is the least squares estimator of â₂, the coefficient of X₂?

 

Show the formulas and the computations. You can check your work with Excel or other statistical software.

 

Why are we being asked for alpha first, when we need beta1 and beta2 to find alpha? Am I misunderstanding the question? This is done again in Module 10.

Did anyone else get alpha = -0.222?

[Edit}Finally figured out the excel regression pack and was able to back into the answers to my questions

There are 16 observations, but only four separate values for X1 and X2. I am getting 0 for X1* and X2* either way, but for X1*^2 and X2*^2 should I be summing the Square of all 16 observations, (i.e. each X* gets counted four times)?

[Edit] Yes I should be



The book does show the steps of the calculation on the prestige page - it only gives the results, and I can't find the actual data to see if i can replicate the results.



EDIT:
Should the sum of the X1* squared (that is the sum of (x sub i minus x bar)) be equal to 5 or 20?
[Edit] 20


If I set it equal to 5 then using that logic the sum of x1*is equal to 0, and the sum of x2* is equal to 0, and B1 and B2 are both 0. Is this correct?
[Edit] Nope - it should be equal to 20 as mentioned above

I got alpha = -0.2221875 while beta1 = 1.069725 and beta2 = -1.065975. Does anyone got the same answers as mine?

Hello. I have a question on just how the homework is supposed to be presented when it is sent in. Are we expected to do all the formulas by hand, or can we show the formulas and what we are computing with Excel doing the actual computation? Thank you!

[NEAS: Computations can be done with Excel; no need to do any work by hand.]

Can you please explain the following:
1) If two explanatory variables are highly correlated, does adding the second explanatory
variable raise or lower the estimated standard deviation of the residuals of the regression?
2) If two explanatory variables are uncorrelated and each is correlated with the dependent
variable, does adding the second explanatory variable raise or lower the estimated standard deviation of the residuals?

[NEAS: The issues are important but subtle. Fox has good explanations.

 

(1) Adding explanatory variables raises the R² but not necessarily the adjusted (corrected) R².

 

See Section 5.2.3 on pages 92-94.

 

(2) Adding a correlated explanatory variable may raise the standard error of the estimator (not the regression).

 

See Section 6.2.2 on pages 106-110 and Section 6.3 on pages 110-112.

 

Illustration: Suppose we regress the personal auto loss cost trend on inflation. If we regress on a single inflation index, such as the CPI or the medical CPI, and we have extensive data with little random fluctuation, the standard error of the regression is low and the standard error of the estimator is low. If we regress on both inflation indices (which are highly correlated), the standard error of the regression will probably decline a bit but the standard error of the estimators will increase.]

 

 

 

I use the following formula to calculate the Part A:

A = Ybar - B1X1bar - B2X2bar

I got A equals to -0.21281 which is also Ybar. But the regession sheet from Excel shows A equals to -0.2221875. Could you tell me why? Thanks!

How do you use Excel to do regression analysis with 2 indepenent variables and 1 dependent variable?

When I click on Data Analysis, it doesn't give option for multivariate regression...

[NEAS: The x-variable can be a matrix with up to 16 columns, for 16 explanatory variables. The form is does not say this explicitly, and the help is not of much help; try it to see how it works.]

You can also use RExcel add in. It will save a lot of time writing code. However, it'll take a bit of time trying to figure out how to use it. Or you could get the Analysis data tool pack. By itself, Excel is somewhat ill equipped to handle advanced statistical analysis.