The Elsmar Cove Forum How to interpret a Linear Regression in Minitab?
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#1
6th April 2012, 09:11 PM
 staykov Shy Poster (1 to 5 Posts)   Registration Date: Apr 2012 Posts: 2 Thanks Given to Others: 1 Thanked 0 Times in 0 Posts Karma Power: 9 Karma: 10
How to interpret a Linear Regression in Minitab?

Hello, I have to do a finance project and am really struggling here. I already passed the deadline and have 1 more week to do it, or I'll get 0 marks

I am doing Purchasing power parity and have to make a regression analysis, using minitab. One of the tests that I am doing is to investigate the relationship between 'The change in exchange rates' versus 'The difference in inflation rates' of two countries. I've done the regression, but now I have to say whether the numbers are good or bad and to draw implications from it. I've searched the web, but everything is very incomprehensible... Here is the regression that I've made and I believe that it is correctly done. Can someone explain what the results of the test mean?
Quote:
 The regression equation is Change in exchange rates = - 0,0131 + 0,00357 Inflation difference Predictor Coef SE Coef T P Constant -0,013144 0,002931 -4,48 0,000 Inflation difference 0,003570 0,001845 1,94 0,055 S = 0,0302862 R-Sq = 3,1% R-Sq(adj) = 2,2% Analysis of Variance Source DF SS MS F P Regression 1 0,0034353 0,0034353 3,75 0,055 Residual Error 119 0,1091531 0,0009173 Total 120 0,1125885 Unusual Observations Change in Inflation exchange Obs difference rates Fit SE Fit Residual St Resid 8 1,13 -0,08764 -0,00910 0,00296 -0,07854 -2,61R 12 1,57 -0,07456 -0,00753 0,00334 -0,06703 -2,23R 14 -4,38 -0,15538 -0,02877 0,00949 -0,12661 -4,40RX 18 6,62 -0,03359 0,01048 0,01154 -0,04407 -1,57 X 27 -3,98 0,00050 -0,02736 0,00879 0,02785 0,96 X 31 5,37 0,00034 0,00604 0,00932 -0,00569 -0,20 X 35 0,72 -0,10906 -0,01056 0,00277 -0,09850 -3,27R 85 1,07 0,06067 -0,00934 0,00292 0,07001 2,32R 120 1,18 -0,06993 -0,00892 0,00299 -0,06101 -2,02R R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large leverage.

#2
7th April 2012, 10:09 AM
 Miner Forum Moderator   Registration Date: Apr 2002 Location: Greater Milwaukee area, Wisconsin Posts: 3,393 Thanks Given to Others: 589 Thanked 1,966 Times in 1,245 Posts Blog Entries: 16 Karma Power: 424 Karma: 18274
Re: How to interpret a Linear Regression in Minitab?

You should always begin a regression analysis by graphing the two variables. There could be a curve relationship that will not show up in linear regression.

There are several thing to review on the Session window output.
• Look at the p-values for each variable. Your p-value is 0.055. This is worth investigating. Most people use 0.05 or 0.10 as the threshold for significance.
• Look at the R^2 values. Yours are extremely low. This means that the model is a very poor fit and is not useful for prediction. This can be caused by missing variables, and/or overlooking a curvilinear relationship.
• Look at the list of unusual observations. You have a lot of influential (high leverage) data points (potential outliers) and points with large residuals. You should post your Residual diagnostics graphs.

Overall, you have one possibility for a relationship, but your model of the relationship is not useful.

__________________

"A fool can learn from his own experiences; the wise learn from the experience of others." - Democritus, 460-370 B.C.

Last edited by Miner; 7th April 2012 at 10:54 AM.
 Thank You to Miner for your informative Post and/or Attachment!
#3
7th April 2012, 04:06 PM
 staykov Shy Poster (1 to 5 Posts)   Registration Date: Apr 2012 Posts: 2 Thanks Given to Others: 1 Thanked 0 Times in 0 Posts Karma Power: 9 Karma: 10
Re: How to interpret a Linear Regression in Minitab?

So do you suggest I should try to look for a relationship between other variables? What do I have to look for to get a better analysis?

p-values between 0.05 and 0.1 and high R^2 values?

Also, I am doing this over a 10-year period and checked whether I have some missing data, but this is not the case. Whatever I am testing I get unusual observations...
#4
7th April 2012, 08:24 PM
 Miner Forum Moderator   Registration Date: Apr 2002 Location: Greater Milwaukee area, Wisconsin Posts: 3,393 Thanks Given to Others: 589 Thanked 1,966 Times in 1,245 Posts Blog Entries: 16 Karma Power: 424 Karma: 18274
Re: How to interpret a Linear Regression in Minitab?

You begin by establishing your alpha value, or the level of risk that you are willing to tolerate of making a Type 1 error (rejecting the null hypothesis in error; See post 15 of this thread). If the p-value is less than alpha, you reject the null hypothesis (For linear regression, the null hypothesis is that the coefficient is zero).

If your alpha value is set at 0.10, you reject the null hypothesis. If set at 0.05, you fail to reject the null hypothesis. If this is exploratory analysis with low risk use 0.1. If you will make decisions of moderate risk, use 0.05. High risk, use 0.01.

Without seeing you data, I can only speculate. The problem might be missing variables, a curvilinear/nonlinear relationship, or both. Graphing the data will tell you whether you have a curvilinear (polynomial) or nonlinear relationship. If you do not, look for additional predictor variables.

__________________

"A fool can learn from his own experiences; the wise learn from the experience of others." - Democritus, 460-370 B.C.

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