Parametric Inference for Linear Regression
Parametric inference is commonly used in analyzing regression. Lets say you have a dataset, with two variables. You want to create a regression model that predicts one variable based on the other. Here’s an example:
R
# Sample datax <- c(1, 2, 3, 4, 5)y <- c(2, 3, 4, 5, 6)# Fit a linear regression modelmodel <- lm(y ~ x)# Summary of the regression modelsummary(model) |
Output:
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5
3.395e-16 -3.543e-16 -1.716e-16 4.793e-17 1.384e-16
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.00e+00 3.27e-16 3.058e+15 <2e-16 ***
x 1.00e+00 9.86e-17 1.014e+16 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.118e-16 on 3 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 1.029e+32 on 1 and 3 DF, p-value: < 2.2e-16
To fit the linear regression model the lm function is utilized. This parametric inference technique assumes a linear relationship between x and y. Estimates the coefficients (intercept and slope) of the equation. The summary function provides information about the model, including estimates, standard errors, t values and p values.
Parametric Inference with R
Parametric inference in R involves the process of drawing statistical conclusions regarding a population using a parametric statistical framework. These parametric models make the assumption that the data adheres to a specific probability distribution, such as the normal, binomial, or Poisson distributions, and they incorporate parameters to characterize these distributions.
It is a technique that involves making assumptions, about the probability distribution underlying your data. Based on these assumptions you can then draw conclusions. Make inferences about population parameters. In the R programming language parametric inference is frequently employed for tasks such, as hypothesis testing and estimating parameters.
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