# Difference between glm and lm in R

Difference between glm and lm in R, In R, how do you tell the difference between lm and glm?

When building intervals in lm, the t-distribution is used, but in glm, the normal distribution is used.

Longer answer: The glm function fits the model via MLE, but you end up with OLS estimates due to the assumption you made about the link function (in this case normal).

## What is a glm Anova, exactly?

While maintaining all other predictors constant, a general linear model, also known as a multiple regression model, generates a t-statistic for each predictor as well as an estimate of the slope associated with the change in the outcome variable.

## When is it fair to employ a general linear model?

To see if the means of two or more groups differ, use the General Linear Model. Random factors, covariates, or a mix of crossing and nested factors can all be used.

How to find a Trimmed Mean in R » finnstats

Stepwise regression can also be used to help determine the model.

## What is the difference between glm and lm?

lm is good for models like Y = XB + e, where eNormal ( 0, s2 ). glm fits models of the type g(Y) = XB + e, where g() and e’s sample distribution must be given. The “link function” is the name given to the function ‘g.’

For fitting linear models, the computer language R provides the following functions:

1. lm — This function is used to fit linear models.

The syntax for this function is as follows:

`lm(formula, data, …)`

where:

formula: The formula for the linear model (e.g. y ~ x1 + x2)

data: The name of the data frame that contains the data

2. glm — This is a tool for fitting generalized linear models.

The syntax for this function is as follows:

`glm(formula, family=gaussian, data, …)`

where:

formula: The formula for the linear model (e.g. y ~ x1 + x2)

family: To fit the model, choose a statistical family. Gaussian is the default, however, there are also binomial, Gamma, and Poisson choices.

data: The name of the data frame in which the data is stored.

The only difference between these two functions is that the glm() function includes a family argument.

When you use lm() or glm() to fit a linear regression model, the results will be identical.

The glm() function, on the other hand, can be used to fit more sophisticated models like:

Logistic regression (family=binomial)

Poisson regression (poisson=family)

The examples below demonstrate how to utilize the lm() and glm() functions in practice.

## Using the lm() Function in Practice

The lm() method is used to fit a linear regression model in the following code:

fit a model of multiple linear regression

`model <- lm(mpg ~ disp + hp, data=mtcars)`

Now we can view the model summary

`summary(model)`
```Call:
lm(formula = mpg ~ disp + hp, data = mtcars)
Residuals:
Min      1Q  Median      3Q     Max
-4.7945 -2.3036 -0.8246  1.8582  6.9363
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.735904   1.331566  23.083  < 2e-16 ***
disp        -0.030346   0.007405  -4.098 0.000306 ***
hp          -0.024840   0.013385  -1.856 0.073679 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.127 on 29 degrees of freedom
Multiple R-squared:  0.7482,       Adjusted R-squared:  0.7309
F-statistic: 43.09 on 2 and 29 DF,  p-value: 2.062e-09```

## Using the glm() Function in Examples

Using the glm() method, the following code shows how to fit the exact same linear regression model.

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model multivariate linear regression

`model <- glm(mpg ~ disp + hp, data=mtcars)`

Let’s view the model summary

`summary(model)`
```Call:
glm(formula = mpg ~ disp + hp, data = mtcars)
Deviance Residuals:
Min       1Q   Median       3Q      Max
-4.7945  -2.3036  -0.8246   1.8582   6.9363
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.735904   1.331566  23.083  < 2e-16 ***
disp        -0.030346   0.007405  -4.098 0.000306 ***
hp          -0.024840   0.013385  -1.856 0.073679 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for gaussian family taken to be 9.775636)
Null deviance: 1126.05  on 31  degrees of freedom
Residual deviance:  283.49  on 29  degrees of freedom
AIC: 168.62
Number of Fisher Scoring iterations: 2```

The coefficient estimates and standard errors of the coefficient estimates are identical to what the lm() function produces.

Note that we can also fit a logistic regression model with the glm() function by providing family=binomial as follows.

Let’s fit the logistic regression model

`model <- glm(am ~ disp + hp, data=mtcars, family=binomial)`

Okay, now see the model summary

`summary(model)`
```Call:
glm(formula = am ~ disp + hp, family = binomial, data = mtcars)
Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.9665  -0.3090  -0.0017   0.3934   1.3682
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  1.40342    1.36757   1.026   0.3048
disp        -0.09518    0.04800  -1.983   0.0474 *
hp           0.12170    0.06777   1.796   0.0725 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 43.230  on 31  degrees of freedom
Residual deviance: 16.713  on 29  degrees of freedom
AIC: 22.713
Number of Fisher Scoring iterations: 8```

We may also fit a Poisson regression model using the glm() function by providing family=poisson as follows.

fit Poisson regression model

```model <- glm(am ~ disp + hp, data=mtcars, family=poisson)
summary(model)```
```Call:
glm(formula = am ~ disp + hp, family = poisson, data = mtcars)
Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.1266  -0.4629  -0.2453   0.1797   1.5428
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.214255   0.593463   0.361  0.71808
disp        -0.018915   0.007072  -2.674  0.00749 **
hp           0.016522   0.007163   2.307  0.02107 *
---Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 23.420  on 31  degrees of freedom
Residual deviance: 10.526  on 29  degrees of freedom
AIC: 42.526
Number of Fisher Scoring iterations: 6```

summarize in r, Data Summarization In R » finnstats

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