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There are conditions linked with linear regression, just as there are with each approach we meet. Linearity, nearly normal residuals, and constant variability are the three criteria.
The first is linearity, which states that the explanatory and response variables should have a linear connection. Because we're using a liner model to predict the response variable from the explanatory variable, this makes sense. To see if the linearity criterion has been satisfied. A scatter plot of the data or a residuals plot can be used.
Near normal residuals is the second requirement, which states that residuals should be almost normally distributed and centered at zero. If there are unusual observations that do not follow the trend of the rest of the data, this condition may not be met. A histogram of a normal probability plot of residuals can be used to verify this criterion.
The last condition is constant variability, which says that variability of points around the least squares line should be roughly constant. This implies that the variability of residuals around the zero line should be roughly constant as well. This condition is also called homoscedasticity. And we can check this using a residuals plot.
It's a bit of an art to check regression diagnostics. It takes a lot of practice to be able to identify whether or not a condition has been met.
After you've double-checked your conditions and determined that a linear model is acceptable for your data and for modeling the relationship between your response and your explanatory factors, the following step is to assess the model's fit. To put it another way, how well it matches your data. And for that, we present R squared, a new metric. R squared is the most popular method for evaluating the fit of a linear model. The square of the correlation coefficient is used to calculate this. The R squared informs us how much of the response variable's variability is explained by the model.Variables not included in the model account for the rest of the variability.
And the R squared value, which is the square of the correlation coefficient, will always be a number between zero and one, corresponding to the percentage of the variability in the response variable that the model explains. Calculating R squared is simple if you know your correlation coefficient. So, if you're going from R squared to R, you should use your calculator or computation to get the numerical answer first, but then examine the relationship between the variables.A scatter plot illustrating the relationship to evaluate if the correlation coefficient should have a positive or negative sign.
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