Linear Regression Flashcards
What is linear regression?
The process of calculating the equation of the line that best represents or fits the data.
What is the purpose of the line of best fit in linear regression?
To make predictions about values that are not in the original dataset.
In the diamond weight and price example, what is the explanatory variable?
The weight (carats) of the diamond.
In the diamond weight and price example, what is the response variable?
The price of the diamond.
What does the best-fit line represent in a scatterplot?
The line that lies closer than any other possible line to all of the points in the scatterplot.
What point does the line of best fit always pass through?
The mean for X and the mean for Y.
What does a positive correlation indicate about the slope of the regression line?
The slope value will be positive, indicating the line moves uphill from left to right.
What is the general equation for the regression line?
Y with overparenthesis on top equals bX + a.
What does ‘b’ represent in the regression equation?
The slope of the line or the rate of change.
What does ‘a’ represent in the regression equation?
The y-intercept of the line.
What does the term ‘r squared’ refer to?
The coefficient of determination, measuring the proportion of variance accounted for by the model.
How is the proportion of variance accounted for calculated?
By squaring the correlation coefficient (r).
What does a larger r squared value imply?
A stronger model of regression and more precise predictions.
How is the statistical significance of the regression equation assessed?
By calculating the F ratio and p-value.
What does a coefficient of determination of r squared = 0.604 signify in the diamond price example?
60.4% of the variability in the price can be predicted from its weight.
What is multiple regression?
Finding the best-fit equation for three or more variables, one response variable and two or more explanatory variables.
What percentage of variability in the exam score can be predicted from hours spent studying if r squared = 0.6724?
67.24%.
