# multreg: A multiple regression analysis using individual data In rpsychi: Statistics for psychiatric research

## Description

`multreg` conducts a multiple regression analysis using individual data.

## Usage

 `1` ```multreg(formula, data, sig.level = 0.05, digits = 3) ```

## Arguments

 `formula` two-sided formula; the left-hand-side of which gives one dependent variable containing a numeric variable, and the right-hand-side of several independent variables containing a numeric variable `data` a data frame contains the variables in the `fomrmula` `sig.level` a numeric contains the significance level (default 0.05) `digits` the specified number of decimal places (default 3)

## Details

This function conducts a multiple regression analysis using individual data. The dependent variable and independent variables should be a numeric vector. In this function, you cannot specify any interaction nor any curvilinear effect. Statistical power is calculated using the following specifications:

(a) small (R^{2} = 0.02), medium (R^{2} = 0.13), and large (R^{2} = 0.26) population effect sizes, according to the interpretive guideline for effect sizes by Cohen (1992)

(b) sample size specified by `data`

(c) significance level specified by `sig.level`

(d) numbers of independent variable specified by `formula`

## Value

 `samp.stat` returns the means and unbiased standard deviations `corr.partial.corr` returns a product-moment correlation matrix (lower triangle) and a partial correlation matrix given all remaining variables (upper triangle) `corr.confidence` returns lower and upper confidence limits (lower and upper triangles, respectively) `omnibus.es` returns a coefficient of determination and its' confidence interval `raw.estimates` returns partial regression coefficients, their confidence intervals, and standard errors `standardized.estimates` returns standardized partial regression coefficients, their confidence intervals, and standard errors `power` returns statistical power for detecting small (R^{2} = 0.02), medium (R^{2} = 0.13), and large (R^{2} = 0.26) population effect sizes

## Author(s)

Yasuyuki Okumura
Department of Social Psychiatry,
National Institute of Mental Health,
National Center of Neurology and Psychiatry
yokumura@blue.zero.jp

## References

Cohen J (1992) A power primer. Psychological Bulletin, 112, 155-159.

Cohen J, Cohen P, Aiken LS (2003) Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed). Mahwah, NJ: Erlbaum.

Smithson M (2001) Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals, 61, 605-632.

`multreg.second`, `samplesize.rsq`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```##Cohen (2003) Table 3.5.1 dat <- data.frame( salary = c(51876, 54511, 53425, 61863, 52926, 47034, 66432, 61100, 41934, 47454, 49832, 47047, 39115, 59677, 61458, 54528, 60327, 56600, 52542, 50455, 51647, 62895, 53740, 75822, 56596, 55682, 62091, 42162, 52646, 74199, 50729, 70011, 37939, 39652, 68987, 55579, 54671, 57704, 44045, 51122, 47082, 60009, 58632, 38340, 71219, 53712, 54782, 83503, 47212, 52840, 53650, 50931, 66784, 49751, 74343, 57710, 52676, 41195, 45662, 47606, 44301, 58582), pubs = c(18, 3, 2, 17, 11, 6, 38, 48, 9, 22, 30, 21, 10, 27, 37, 8, 13, 6, 12, 29, 29, 7, 6, 69, 11, 9, 20, 41, 3, 27, 14, 23, 1, 7, 19, 11, 31, 9, 12, 32, 26, 12, 9, 6, 39, 16, 12, 50, 18, 16, 5, 20, 50, 6, 19, 11, 13, 3, 8, 11, 25, 4), cits = c(50, 26, 50, 34, 41, 37, 48, 56, 19, 29, 28, 31, 25, 40, 61, 32, 36, 69, 47, 29, 35, 35, 18, 90, 60, 30, 27, 35, 14, 56, 50, 25, 35, 1, 69, 69, 27, 50, 32, 33, 45, 54, 47, 29, 69, 47, 43, 55, 33, 28, 42, 24, 31, 27, 83, 49, 14, 36, 34, 70, 27, 28) ) multreg(salary~ pubs + cits, data=dat) ```