A.     Estimate the parameter ö by regression analysis.

B.     What are 95% confidence intervals for the value of ö?

C.    You initially believed that ö is 50%. Should you reject this assumption?

 

The time series course does not teach regression analysis. You are assumed to know how to run a regression analysis, and you must run regressions for the student project.

 

Use the Excel regression add-in. The 95% confidence interval is the estimated â ± the t-value × the standard error of â. The t-value depends on the number of observations. Excel has a built-in function giving the t-value for a sample of N observations.

 

 

 

I need a quick refresher on the confidence intervals with the t-test. I ran the regression tool in excel and got the slope variable to be .121. I notice the tool also spits out a 95% confidence interval - but it doesn't seem to match what I am doing for the t-test interval (based on the instructions in the hw).

Is my interval correct? .121+/- 4.9228*.02457

All of these inputs came from the excel tool - am i supposed to be calculating anything on my own? Thanks in advance for the help.

[NEAS: This dialogue explains the procedure.

Jacob: What are the X and Y values of this regression?

Rachel: Each Yt is a function of Yt-1.

The X values are {0.44 1.05 0.62 0.72 1.08 1.24 1.42 1.35}.

The Y values are {1.05 0.62 0.72 1.08 1.24 1.42 1.35 1.50}.

Write the regression equation as Yt = A + B × Yt-1. Excel gives you indicated parameters and t-values.

For the time series final exam, no expertise in regression analysis is assumed. But you must run regressions to estimate autoregressive processes for the student project.

The indicated φ of this regression is close to 0.5, and we would not reject a null hypothesis that φ = 50%. Use the Excel regression add-in to compute the exact φ. The homework shows that you can use the Excel add-in.

You can use any statiscal package, such as SAS or R. They give the same values for the parameter.]

Is the calculation for the 95% confidence interval given in the homeowork suppose to be equal to the confidence interval that comes from running the regression in Excel?  Mine do not equal each other.  Thanks.

I think you guys are using the T-stat from the regression output for your confidence interval.  I believe you should use the T-value.  You can find the T-value by using the "TINV" distribution in Excel, with the probability required for the confidence interval (ex 1-.95 and proper degrees of freedom.  Using this gives the same confidence interval as the regression output.

We are able to use the regression feature of Excel with the model of y = a+bx. But the first-order case for AR(1) models is of the form

Y_t - mu = phi(T_{t-1} - mu) + e_t

How is mu being considered in the y = a +bx model? If b is phi, then what does a represent? Would e_t represent the RSS term?

Thanks.

Doc, if I got any of the assignments incorrect, it was this one.  That being said, I converted Y_t into Y-bar_t, to create a zero-mean function of time.  I used homework 10's method to find r₁ for what I feel constitute's "regression analysis".  This is the estimate of phi-hat.

For part B I used Excel's regression to find the confidence interval, if your estimate is within the 95% confidence interval, then it is quite likely that you wouldn't reject this assumption.

RDH

is the Y-bar equals to the average of Yt?
so i get the phi-hat equals to 0.490371934 with the equation on page 155, while excel shows the coefficient of Yt-1 is 0.614716172
by using the regression analysis
and the 95% confidence interval is [0.158126732,1.071305612]

why is the difference that large?

and what is the intercept coefficient for?
y=a+bt
i know it is stand for a for a linear regression

Following the NEAS post I entered

X as {0.44 1.05 0.62 0.72 1.08 1.24 1.42 1.35}.

and Y as {1.05 0.62 0.72 1.08 1.24 1.42 1.35 1.50}.

After I did the regression I got 0.5425 as the coeffecient for X which would be the phi value. And {-0.16579,1.25081} as the 95% confidence level for phi.

When I perform the phi hat calculation on page 155 of the text I got .4904. Is this just an estimation and that is why it does not match the answer from the regression or did I set up the regression wrong?

 

I made the same mistake until I read the section more carefully.

It has to do with the "conditional" part of the explanation, I believe. I got the same .49 value when I calculated Y-bar using all 9 values. Based on the equation at the top of page 155, Y-bar should be the average of the first 8 Y values only. This makes sense based on the sentence right above equation 7.2.2 on page 154 too and the basic idea that we're using the Y_t_1 observations as X and Y_t observations as Y.

Doing this results in the same estimate of .54 that the Excel regression tool returns.

should we calculate the confidence intervals as stated in the HW?  i've been trying real hard but could not replicate the results from Excel as far as the confidence intervals are concerned

i'm able to estimate the phi manually and replicate Excel output...

anybody please help?!  i really like to understand so that if this same thing is asked in the Final Exam, I could answer. thanks! 

[NEAS: Cryer and Chan use z-values for confidence intervals, not t-values, to make the logic simpler. They assume the paramters are known with certainty. The proper confidence intervals use t-values. The final exam problems give you the t-value or z-value to use.]