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# 统计代写|R语言代写r project代考|MSC1090 Fitting linear models

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## 统计代写|R语言代写r project代考|Fitting linear models

In $\mathrm{R}$, the models to be fitted are described by “model formulas” such as $\mathrm{y} \sim \mathrm{x}$ which we read as $y$ is explained by $x$. Model formulas are used in different contexts: fitting of models, plotting, and tests like $t$-test. The syntax of model formulas is consistent throughout base $\mathrm{R}$ and numerous independently developed packages. However, their use is not universal, and several packages extend the basic syntax to allow the description of specific types of models.

As most things in $\mathrm{R}$, model formulas can be stored in variables. In addition, contrary to the usual behavior of other statistical software, the result of a model fit is returned as an object, containing the different components of the fit. Once the model has been fitted, different methods allow us to extract parts and/or further manipulate the results obtained by fitting a model. Most of these methods have implementations for model fit objects for different types of statistical models. Consequently, what is described in this chapter using linear models as examples, also applies in many respects to the fit of models not described here.

The $\mathrm{R}$ function $1 \mathrm{~m}($ ) is used to fit linear models. If the explanatory variable is continuous, the fit is a regression. If the explanatory variable is a factor, the fit is an analysis of variance (ANOVA) in broad terms. However, there is another meaning of ANOVA, referring only to the tests of significance rather to an approach to model fitting. Consequently, rather confusingly, results for tests of significance for fitted parameter estimates can both in the case of regression and ANOVA, be presented in an ANOVA table. In this second, stricter meaning, ANOVA means a test of significance based on the ratios between pairs of variances.

If you do not clearly remember the difference between numeric vectors and factors, or how they can be created, please, revisit chapter 2 on page 17.

## 统计代写|R语言代写r project代考|Regression

In the example immediately below, speed is a continuous numeric variable. In the ANOVA table calculated for the model fit, in this case a linear regression, we can see that the term for speed has only one degree of freedom (df).

In the next example we continue using the stopping distance for cars data set included in R. Please see the plot on page 125.
data(cars)
is. factor (cars\$speed) ## [1] FALSE is. numeric(cars$\ speed)
## [1] TRUE
We then fit the simple linear model $y=\alpha \cdot 1+\beta \cdot x$ where $y$ corresponds to stopping distance (dist) and $x$ to initial speed (speed). Such a model is formulated in $\mathrm{R}$ as dist $\sim 1+$ speed. We save the fitted model as $\mathrm{fm} 1$ (a mnemonic for fitted-model one).
$\mathrm{fm} 1<-1 \mathrm{~m}$ (dist $\sim 1+$ speed, data=cars)
class (fm1)
## [1] “7m”
The next step is diagnosis of the fit. Are assumptions of the linear model procedure used reasonably close to being fulfilled? In $\mathrm{R}$ it is most common to use plots to this end. We show here only one of the four plots normally produced. This quantile vs. quantile plot allows us to assess how much the residuals deviate from being normally distributed.

## 统计代写|R语言代写 r project代考|Regression

# [1] TRUE

$\mathrm{fm} 1<-1 \mathrm{~m}$ (距离 $\sim 1+$ speed, data=cars)
class $(\mathrm{fml})$
# [1] “7m”

## MATLAB代写

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