# Multiple individual regressions

Hello everyone, I am new to R studio and I cannot find the right code to solve my issue.

I have time series data and I want to use fund's returns as dependent variable and some factors as indipendent variables. Given the fact that I have hundreds of funds, I would lose a lot of time performing each regression manually. Is possible fixing the indipendent variables, performing the regression for each fund automatically and saving the output?

Thank you!

Yes, it is possible, but to help us help you, could you please prepare a reproducible example (reprex) illustrating your issue? Please have a look at this guide, to see how to create one:

I created some hypothetical data. Does this work for you?

df <- data.frame( x1 = runif(30), x2 = runif(30), y = runif(30) ) # hypothetical data
summary <- data.frame()
n <- ncol(df) - 1
indepvars <- colnames(df[1:n])
indepvars
for(i in 1:n) {
formula <- paste0("y ~ ", indepvars[i])
model <- lm(formula, df)
summary[i,1] <- colnames(df[i])
summary[i,2] <- model\$coefficients[1]
summary[i,3] <- model\$coefficients[2]
s <- summary(model)
}
colnames(summary) <- c("Indep var", "Intercept", "Slope", "Adj R^2")
summary

[1] "x1" "x2"
Indep var Intercept Slope Adj R^2
1 x1 0.8357128 -0.38962175 0.12795058
2 x2 0.6683086 -0.07937175 -0.02845706

2 Likes

Dear fcas80,

With your code, I see that y is the dependent variable and x1, x2... is the independent variables.
However, I want to regress each variable x1, x2... on the independent variable y. Variable y in my data set is the market return, and I want to regress all the funds individually on the market return to obtain alphas (intercept). Is there a solution for this?

Have a nice day.

Here is an example of the dataset where I have date, two mutual funds and the market excess return.

datapasta::df_paste(head(dataframe, 5)[, c('Date','Alfred Berg Global C (NOK)', 'APS Global Equity R', 'mkt-rf')])
data.frame(
check.names = FALSE,
Date = c("2016-01-01","2016-02-01","2016-03-01",
"2016-04-01","2016-05-01"),
`Alfred Berg Global C (NOK)` = c(-0.0708041333333334,0.0115925,0.00619040000000006,
-0.0366933,0.0415465333333334),
`APS Global Equity R` = c(-0.0681767333333333,0.0077110000000001,
0.00870629999999997,-0.00214280000000002,
0.0217895333333334),
`mkt-rf` = c(-0.0743514443678082,-0.00884050754326752,
0.018302499067988,-0.0128197204370558,
0.0391929254039709)
)

I want to regress both of the funds individually on the market return.

I have written the following code for the linear model:

summary(lm(df.t18\$`Alfred Berg Global C (NOK`~ df.t18\$`mkt-rf`))

Is there a way I can do this regression on all the mutual funds at the same time? Now I manually change the name of the dependent variable for every regression, but this is very time consuming.

I appreciate all help I can get!

Is this what you need?

df <- data.frame( y1 = runif(30), y2 = runif(30), x = runif(30) ) # hypothetical data
summary <- data.frame()
n <- ncol(df) - 1
depvars <- colnames(df[1:n])

for(i in 1:n) {
formula <- paste0(depvars[i], " ~ x")

model <- lm(formula, df)
summary[i,1] <- colnames(df[i])
summary[i,2] <- model\$coefficients[1]
summary[i,3] <- model\$coefficients[2]
s <- summary(model)
}
colnames(summary) <- c("Dep var", "Intercept", "Slope", "Adj R^2")
summary

``````library(tidyverse)

sample_df <- data.frame(
check.names = FALSE,
Date = c("2016-01-01","2016-02-01","2016-03-01",
"2016-04-01","2016-05-01"),
`Alfred Berg Global C (NOK)` = c(-0.0708041333333334,0.0115925,0.00619040000000006,
-0.0366933,0.0415465333333334),
`APS Global Equity R` = c(-0.0681767333333333,0.0077110000000001,
0.00870629999999997,-0.00214280000000002,
0.0217895333333334),
`mkt-rf` = c(-0.0743514443678082,-0.00884050754326752,
0.018302499067988,-0.0128197204370558,
0.0391929254039709)
)

sample_df %>%
pivot_longer(-c(`mkt-rf`, Date), names_to = 'Fund', values_to = 'Value') %>%
group_by(Fund) %>%
group_modify(~broom::glance(lm(Value ~ `mkt-rf`, data = .x)))
#> # A tibble: 2 × 13
#> # Groups:   Fund [2]
#>   Fund   r.squ…¹ adj.r…²  sigma stati…³ p.value    df logLik   AIC   BIC devia…⁴
#>   <chr>    <dbl>   <dbl>  <dbl>   <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>   <dbl>
#> 1 Alfre…   0.857   0.809 0.0193    17.9  0.0241     1   13.9 -21.8 -23.0 1.12e-3
#> 2 APS G…   0.904   0.872 0.0127    28.2  0.0130     1   16.0 -26.0 -27.2 4.85e-4
#> # … with 2 more variables: df.residual <int>, nobs <int>, and abbreviated
#> #   variable names ¹​r.squared, ²​adj.r.squared, ³​statistic, ⁴​deviance
``````

Created on 2022-10-26 with reprex v2.0.2

Thank you very much guys.

With your code @andresrcs , is it possible to see the intercept as well?

yes

``````library(tidyverse)

sample_df <- data.frame(
check.names = FALSE,
Date = c("2016-01-01","2016-02-01","2016-03-01",
"2016-04-01","2016-05-01"),
`Alfred Berg Global C (NOK)` = c(-0.0708041333333334,0.0115925,0.00619040000000006,
-0.0366933,0.0415465333333334),
`APS Global Equity R` = c(-0.0681767333333333,0.0077110000000001,
0.00870629999999997,-0.00214280000000002,
0.0217895333333334),
`mkt-rf` = c(-0.0743514443678082,-0.00884050754326752,
0.018302499067988,-0.0128197204370558,
0.0391929254039709)
)

sample_df %>%
pivot_longer(-c(`mkt-rf`, Date), names_to = 'Fund', values_to = 'Value') %>%
group_by(Fund) %>%
group_modify(~broom::tidy(lm(Value ~ `mkt-rf`, data = .x)))
#> # A tibble: 4 × 6
#> # Groups:   Fund [2]
#>   Fund                       term         estimate std.error statistic p.value
#>   <chr>                      <chr>           <dbl>     <dbl>     <dbl>   <dbl>
#> 1 Alfred Berg Global C (NOK) (Intercept) -0.00229    0.00880   -0.260   0.812
#> 2 Alfred Berg Global C (NOK) `mkt-rf`     0.953      0.225      4.23    0.0241
#> 3 APS Global Equity R        (Intercept) -0.000346   0.00580   -0.0596  0.956
#> 4 APS Global Equity R        `mkt-rf`     0.789      0.148      5.31    0.0130
``````

Created on 2022-10-27 with reprex v2.0.2

Thank you very much @andresrcs

One last question:
Is there an easy way to add several explanatory variables in the regression? I want to check for other factors in the stock market, in addition to the market return (mkt-rf). In my dataset, I have added two more explanatory variables, called "SMB" and "HML". These two columns is to the right of the variable "mkt-rf" and I tried running the following code without luck:

dataframe %>%
pivot_longer(-c(`mkt-rf`, Date), names_to = 'Fund', values_to = 'Value') %>%
group_by(Fund) %>%
group_modify(~broom::tidy(lm(Value ~ `mkt-rf`+`SMB`+`HML`, data = .x)))

Do you have a quick answer to this?

Thanks again.

Those variables need to be present in the data as columns not levels of a factor so you need to exclude them from the pivoting as well.

``````dataframe %>%
pivot_longer(-c(`mkt-rf`, Date, SMB, HML), names_to = 'Fund', values_to = 'Value')
``````
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