Re: How to compute p-values associated with regression coefficients from multiple linear regression?

FYI only: An updated MLR function has been added to NCL.
           This includes confidence limits, t-values & p-values.
           The output matches R results. In addition, it
           provides ANOVA information.

http://www.ncl.ucar.edu/Document/Functions/Contributed/reg_multlin_stats.shtml

It will be distributed with NCL 6.2.0 when released.

---
However, since it is an NCL script which will reside in
contributed.ncl, it can be downloaded and used with
just about any version of NCL released over the last 5 years.
It can be obtained from:
http://www.cgd.ucar.edu/~shea/reg_multlin_stats.ncl
Cheers
On 01/13/2014 07:46 AM, Dennis Shea wrote:
> re: "compute the p-value that is associated
>       to each regression coefficient"
>
> Hopefully, someone more knowledgeable than I can help here.
>
> ================================================================
> [1] If you have 'R' available, you could use the following approach.
>      In NCL, create an ascii (or binary, or netCDF) file which can be
>      read by R.  Here it is a sample ascii file.
>
>      The sample data set [KENTUCKY.TXT] is the same as is used
>       in Example 3 at
> http://www.ncl.ucar.edu/Document/Functions/Built-in/reg_multlin.shtml
>
>      Start R, then enter the following
>
>      df = read.table("KENTUCKY.TXT", header=TRUE) # read => data frame
>      df # print contents of 'df'
>
>      mlr <- lm(Y~., data=df)
>      mlr # output results ... this contains the info you want
>          # see 'Coefficients'  and significance
>
>
> +++++++
> Call:
> lm(formula = Y ~ ., data = df)
>
> Coefficients:
> (Intercept)           X1           X2           X3           X4   X5
>    -2.244460     0.005091     0.022573    -0.232804     0.062611 -0.002038
>           X6
>    -0.116584
>
>  > summary(mlr)
>
> Call:
> lm(formula = Y ~ ., data = df)
>
> Residuals:
>      Min      1Q  Median      3Q     Max
> -5.7159 -2.8806 -0.7836  1.2759 22.1562
>
> Coefficients:
>               Estimate Std. Error t value Pr(>|t|)
> (Intercept) -2.244460  11.270778  -0.199  0.84309
> X1           0.005091   0.010959   0.465  0.64458
> X2           0.022573   0.008168   2.764  0.00838 **
> X3          -0.232804   0.175949  -1.323  0.19278
> X4           0.062611   0.020587   3.041  0.00400 **
> X5          -0.002038   0.002186  -0.932  0.35656
> X6          -0.116584   0.072610  -1.606  0.11568
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 5.136 on 43 degrees of freedom
> Multiple R-squared:  0.6136,    Adjusted R-squared:  0.5596
> F-statistic: 11.38 on 6 and 43 DF,  p-value: 1.394e-07
>
> ==========================================================
>
> [2] I don't know how to compute the standard error of the coefficients.
>      That is what is necessary to compute the t-values. Hopefully,
>      someone more knowledgeable than I can help!!!!!
>
>      Attached is an NCL script with a local function that can be reused.
>
>      It does return the (overall) multiple regression coef and
>      the F-statistic.
>
>      The t-value (-> probability) requires the standard error of
>      the coefficients.
>
>
> On 1/8/14, 2:26 PM, Strada, Susanna wrote:
>> Hi,
>>
>> I performed a multiple linear regression analysis using NCL function
>> "reg_multlin" to obtain a 2D (lat,lon) map of standardized regression
>> coefficients (6 independent variables, 30 observations).
>>
>>       N = dimsizes(y)
>>       M = N_vars
>>       X = new( (/M+1,N/), "float" )
>>       X(0,:) = 1.0
>>       X(1,:) = x1
>>       X(2,:) = x2
>>       X(3,:) = x3
>>       X(4,:) = x4
>>       X(5,:) = x5
>>       X(6,:) = x6
>>       beta = reg_multlin(y, X, False)
>>
>> Now, I would like to compute the p-value that is associated to each
>> regression coefficient.
>> I'm thinking about, firstly, computing the t-value by doing the ratio
>> between a regression coefficient and its standard deviation,
>> afterwards I will use the NCL function "betainc" to get the p-value
>> for a Student t-test.
>>
>> My problem is that I don't know how to obtain the standard deviation
>> of each regression coefficient using NCL. I tried to move the
>> "reg_multlin" function in a loop over the number of observations:
>>
>>       do nf = 0,nfils-1,1
>> ->      b_nf(:,nf) = reg_multlin(y, X(:,nf), False)
>>       end do
>>
>>       fAODbeta(ns,ilat,ilon) = beta(1) + 0.
>>       fAODbeta_std(ns,ilat,ilon) = stddev(b_nf(1,:)) + 0.
>>
>> but I get the following error for the line indicated by an arrow (->)
>>
>> fatal:Number of dimensions in parameter (1) of (reg_multlin) is (1),
>> (2) dimensions were expected
>>
>> Could you suggest me how to solve my problem?
>> Or do you know a better way to estimate the p-value associated with
>> each regression coefficients?
>>
>> Many thanks!
>>
>> Best regards,
>> Susanna
>> _______________________________________________
>> ncl-talk mailing list
>> List instructions, subscriber options, unsubscribe:
>> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
>>
_______________________________________________
ncl-talk mailing list
List instructions, subscriber options, unsubscribe:
http://mailman.ucar.edu/mailman/listinfo/ncl-talk