18 Questions
What is the range of the Pearson correlation coefficient?
-1 to 1
If points fall on a straight line with a negative slope, what value would the correlation coefficient have?
-1
What does a correlation of 0 indicate?
Points are not linearly related
How does changing the units of measurement affect the correlation coefficient?
It does not change
What is the sample covariance defined as with respect to bivariate data?
(xi - x)(yi - y)
In an elementary school where shoe size and reading level are measured, what kind of correlation is observed?
Positive correlation
What is Age referred to as in the context of the text?
Lurking variable
Why should we only consider linear relationships in the context of linear regression?
Variables with nonlinear relationships can sometimes be transformed to be linear.
What does a lurking variable cause in the correlation between two variables?
It causes a spurious correlation.
What is the objective of linear regression according to the text?
To fit a straight line to the data.
Which variable is referred to as the response in linear regression?
Output variable
Why are linear relationships preferred over nonlinear ones in certain cases?
Nonlinear relationships can sometimes be closely approximated by linear relationships.
What do the constants β0 and β1 represent in the equation of a straight line y = β1x + β0?
β0 is the y-intercept and β1 is the slope
Why is it challenging to determine the 'best-fitting' line using visual inspection?
Different people will perceive lines differently
What does the least squares line minimize in the context of regression analysis?
Sum of squared deviations from the data
How are the estimated values of β0 and β1 calculated using the least square method?
By minimizing the sum of squared errors
What does yb represent in the context of a regression line with equation y = βb1x + βb0?
Predicted value given an x-variable
Why do we use scatter diagrams before estimating β0 and β1 for regression analysis?
To determine if a linear relationship exists between variables
This quiz covers the calculation and interpretation of the Pearson correlation coefficient, which measures the strength of the linear relationship between two variables. Learn how correlations can range from -1 to 1, with different values indicating the strength and direction of the relationship.
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