# [R] significantly different from one (not zero) using lm

Jeff Newmiller jdnewmil at dcn.davis.CA.us
Sat May 4 18:42:28 CEST 2013

```Parameters are different from functions, and offset is a function. Kindly read the help for that function and the references given there.
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Sent from my phone. Please excuse my brevity.

Elaine Kuo <elaine.kuo.tw at gmail.com> wrote:

>Hello,
>
>Thanks.
>But the parameter offset is new to me.
>Please kindly explain why setting offset to x will give a significant
>test
>of whether the slope coefficient is different from one.
>(I checked the ?lm but still do not understand it well)
>
>Thanks again
>
>Elaine
>
>
>On Wed, May 1, 2013 at 11:12 AM, Thomas Lumley <tlumley at uw.edu> wrote:
>
>> Or use an offset
>>
>> lm( y ~ x+offset(x), data = dat)
>>
>> The offset gives x a coefficient of 1, so the coefficient of x in
>this
>> model is the difference between the coefficient of x in the model
>without
>> an offset and 1 -- the thing you want.
>>
>>     -thomas
>>
>>
>> On Wed, May 1, 2013 at 2:54 PM, Paul Johnson <pauljohn32 at gmail.com>
>wrote:
>>
>>> It is easy to construct your own test. I test against null of 0
>first so I
>>> can be sure I match the right result from summary.lm.
>>>
>>> ## get the standard error
>>> seofb <- sqrt(diag(vcov(lm1)))
>>> ## calculate t. Replace 0 by your null
>>> myt <- (coef(lm1) - 0)/seofb
>>> mypval <- 2*pt(abs(myt), lower.tail = FALSE, df = lm1\$df.residual)
>>>
>>> ## Note you can pass a vector of different nulls for the
>coefficients
>>> myt <- (coef(lm1)  - c(0,1))/seofb
>>>
>>> We could write this into a function if we wanted to get busy.  Not a
>>> little homework exercise, I think.
>>>
>>>
>>>
>>>
>>> > dat <- data.frame(x = rnorm(100), y = rnorm(100))
>>> > lm1 <- lm(y ~ x, data = dat)
>>> > summary(lm1)
>>>
>>> Call:
>>> lm(formula = y ~ x, data = dat)
>>>
>>> Residuals:
>>>     Min      1Q  Median      3Q     Max
>>> -3.0696 -0.5833  0.1351  0.7162  2.3229
>>>
>>> Coefficients:
>>>              Estimate Std. Error t value Pr(>|t|)
>>> (Intercept) -0.001499   0.104865  -0.014    0.989
>>> x           -0.039324   0.113486  -0.347    0.730
>>>
>>> Residual standard error: 1.024 on 98 degrees of freedom
>>> Multiple R-squared: 0.001224,    Adjusted R-squared: -0.008968
>>> F-statistic: 0.1201 on 1 and 98 DF,  p-value: 0.7297
>>>
>>> > seofb <- sqrt(diag(vcov(lm1)))
>>> > myt <- (coef(lm1) - 0)/seofb
>>> > mypval <- 2*pt(abs(myt), lower.tail = FALSE, df = lm1\$df.residual)
>>> > myt
>>> (Intercept)           x
>>> -0.01429604 -0.34650900
>>> > mypval
>>> (Intercept)           x
>>>   0.9886229   0.7297031
>>> > myt <- (coef(lm1) - 1)/seofb
>>> > mypval <- 2*pt(abs(myt), lower.tail = FALSE, df = lm1\$df.residual)
>>> > myt
>>> (Intercept)           x
>>>   -9.550359   -9.158166
>>> > mypval
>>>  (Intercept)            x
>>> 1.145542e-15 8.126553e-15
>>>
>>>
>>> On Tue, Apr 30, 2013 at 9:07 PM, Elaine Kuo
><elaine.kuo.tw at gmail.com>
>>> wrote:
>>>
>>> > Hello,
>>> >
>>> >
>>> >
>>> > I am work with a linear regression model:
>>> >
>>> > y=ax+b with the function of lm.
>>> >
>>> > y= observed migration distance of butterflies
>>> >
>>> > x= predicted migration distance of butterflies
>>> >
>>> >
>>> >
>>> > Usually the result will show
>>> >
>>> > if the linear term a is significantly different from zero based on
>the
>>> > p-value.
>>> >
>>> > Now I would like to test if the linear term is significantly
>different
>>> from
>>> > one.
>>> >
>>> > (because I want to know if the regression line (y=ax+b) is
>significantly
>>> > from the line with the linear term =1 and the intercept =0)
>>> >
>>> >
>>> >
>>> >
>>> > to adjust some default parameters in the function to achieve the
>goal.
>>> >
>>> > Thank you.
>>> >
>>> >
>>> > Elaine
>>> >
>>> >         [[alternative HTML version deleted]]
>>> >
>>> > ______________________________________________
>>> > R-help at r-project.org mailing list
>>> > https://stat.ethz.ch/mailman/listinfo/r-help
>>> > http://www.R-project.org/posting-guide.html
>>> > and provide commented, minimal, self-contained, reproducible code.
>>> >
>>>
>>>
>>>
>>> --
>>> Paul E. Johnson
>>> Professor, Political Science      Assoc. Director
>>> 1541 Lilac Lane, Room 504      Center for Research Methods
>>> University of Kansas                 University of Kansas
>>> http://pj.freefaculty.org               http://quant.ku.edu
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>>
>> --
>> Thomas Lumley
>> Professor of Biostatistics
>> University of Auckland
>>
>
>	[[alternative HTML version deleted]]
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

```