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How to interpret a Linear Regression in Minitab?

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  Post Number #1  
Old 6th April 2012, 09:11 PM

Total Posts: 2
Question 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?
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.
Thank you in advance, I would really appreciate your help

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  Post Number #2  
Old 7th April 2012, 10:09 AM
Miner's Avatar

Total Posts: 3,721
Look! 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.

Last edited by Miner; 7th April 2012 at 10:54 AM.
Thank You to Miner for your informative Post and/or Attachment!
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  Post Number #3  
Old 7th April 2012, 04:06 PM

Total Posts: 2
Re: How to interpret a Linear Regression in Minitab?

Thank you for your answer.
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...
  Post Number #4  
Old 7th April 2012, 08:24 PM
Miner's Avatar

Total Posts: 3,721
Look! 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.

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