Red
If there is a perfect correlation between two variables a and b, then either a caused b or b caused a .
Sometimes true: Variables that are perfectly correlated may be causally related, but they often are not. Correlation does not equal causation.
If there is a perfect correlation between variables in the data, then the correlation coefficient is 1 .
Sometimes true: The correlation coefficient for a perfect correlation could also be -1.
A negative correlation coefficient means that the data points are very random and don’t really fit a linear model.
Sometimes true: The sign of the correlation coefficient gives the direction of the linear relationship. A negative correlation coefficient means that the linear relationship has a negative slope. It is possible to have a negative correlation coefficient that is near , which may indicate that a linear model is not appropriate.
The larger the residual for a given point, the further away the point is from the line of best fit.
Always true: This is part of the definition of residual.
The sum of the residuals for the line of best fit is 0.
Always true: The way that the line of best fit is calculated makes this true in every case.
If the correlation coefficient is positive, then the slope of the line of best fit will probably be positive.
Always true: The sign of the correlation coefficient gives the direction of the relationship.
If the correlation coefficient for a set of data is 0 , then the line of best fit is horizontal.
Never true: A correlation coefficient of 0 means that there is not a linear relationship between the variables.
If the correlation coefficient is very large, then there must be an outlier in the data.
Never true: A large correlation coefficient (near ) means that the variables have a strong, positive relationship.
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Always
A person's shoe size will determine how many siblings they will have.
No, there may be correlation, but it does not necessarily have causation.
To find the value of a residual for a point, (a,b), given a line of best fit, :
Find f(a).
Find b-f(a) .
If the answer is positive, then the point is above the line.
If the answer is negative, then the point is below the line.
Always true: This is a description of the procedure for finding residuals.
A negative residual means that the regression line is very far from the actual data point.
Sometimes true: A negative residual means that the point is below the regression line; sometimes the point may be far from the actual point, but it might not be.
The slope of the linear regression line can be calculated using any two points in the data.
Sometimes true: It is only true if it is a perfect correlation, r=1 or r=-1 .
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A correlation coefficient of 0.68 indicates a strong negative correlation.
Ha! Nope. Never. It's a weak positive correlation.