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Building a statistical model involves a few key steps. First, you collect and prepare your data. Then, you choose the right model for your data, fit the model to your data, and finally, evaluate how well the model performs.
# This code calculates how strongly TV advertising is related to sales using a correlation test.
coefficient <- cor.test(advertising$TV, advertising$Sales)
coefficient$estimate
One assumption of linear regression is that the relationship between your variables is linear. This means that as one variable changes, the other variable should change in a consistent way.
# This code creates a box plot to visualize the distribution of sales data.
plot <- advertising %>%
ggplot(aes(sales)) +
geom_boxplot()
Outliers are data points that are significantly different from others. You can find them visually by creating scatter plots, or by fitting a model and checking if some points have unusual residuals.
# This code fits a simple linear regression model to predict sales based on podcast data.
model <- lm(sales ~ podcast, data = train)
# This code fits a more complex model using both podcast and TV data as predictors.
model2 <- lm(sales ~ podcast + TV, data = train)
To build a linear regression model, you use the `lm()` function in R. This function helps you understand how one variable predicts another, and you can assess the strength of this relationship using the model's summary.
# This code provides a summary of the model, including the Residual Standard Error (RSE).
summary(model)
# This code retrieves the Residual Standard Error directly.
sigma(model)
The Residual Standard Error (RSE) measures how well your model fits the data. It tells you how far off your predictions are from the actual values. A lower RSE means a better fit.
# This code calculates the R Squared value, which shows how well the model explains the variability in the data.
summary(model)$r.squared
R Squared is a metric that shows the proportion of variance in the outcome variable that is explained by the predictor variables. A higher R Squared value indicates a better fit of the model to the data.
Residuals are the differences between the actual values and the values predicted by your model. You can visualize them using plots like box plots to see if there are any unusual patterns or outliers.
LOESS (Locally Estimated Scatterplot Smoothing) is a technique used to visualize data trends. Unlike linear regression, it can handle more complex, non-linear relationships between variables.
In multiple linear regression, you use several predictor variables to explain the outcome variable. Each predictor has its coefficient, which tells you how much it contributes to the outcome.
In simple linear regression, there is just one predictor variable. The coefficient shows how much this single predictor variable affects the outcome variable.
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