Linear Regression and Multivariate Linear Regression: Flashcards
What is the main goal of linear regression?
To predict the value of one variable based on another.
Write the equation of a simple linear regression.
y=β_0+β_1x
What do the coefficients 𝛽_0 and 𝛽_1 represent?
β_0 : y-intercept; 𝛽_1: slope of the line.
What is the residual in linear regression?
The difference between the observed value and the predicted value.
What is the purpose of the R-squared value?
It measures the proportion of variance explained by the model.
What does a high R-squared value indicate?
A strong linear relationship between the variables.
What is the adjusted R-squared value?
It accounts for the number of predictors in the model.
How is the F-statistic used in linear regression?
To test if the model fits the data better than a model without predictors.
Why might you use multiple linear regression instead of simple linear regression?
To assess the impact of multiple predictors on the outcome variable.
What does a significant p-value for a regression coefficient mean?
The predictor variable significantly affects the outcome.
Why do we plot data before running a linear regression?
To visually assess the relationship and ensure linearity.
What assumptions does linear regression make about the data?
Linearity, independence, homoscedasticity, and normality of residuals.
In multiple regression, what does the term 𝛽_2𝑥_2 represent?
The effect of 𝑥_2 on the outcome, holding other predictors constant.
What does the slope of the regression line indicate?
The rate of change in the outcome variable for a unit change in the predictor.
Beyond the topic: How can regression be used to analyze trends in environmental data over time?
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