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Correlation and Linear Regression: Pearson Correlation Coefficient

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Correlation and Linear Regression: Pearson Correlation Coefficient

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Questions and Answers

What is the range of the Pearson correlation coefficient?

-2 to 0

0 to 2

-1 to 1 (correct)

1 to 3

If points fall on a straight line with a negative slope, what value would the correlation coefficient have?

-1 (correct)

What does a correlation of 0 indicate?

Strong linear relationship

Perfect negative correlation

Points are not linearly related (correct)

Perfect positive correlation

How does changing the units of measurement affect the correlation coefficient?

It does not change Signup and view all the answers

What is the sample covariance defined as with respect to bivariate data?

(xi - x)(yi - y) Signup and view all the answers

In an elementary school where shoe size and reading level are measured, what kind of correlation is observed?

Positive correlation Signup and view all the answers

What is Age referred to as in the context of the text?

Lurking variable Signup and view all the answers

Why should we only consider linear relationships in the context of linear regression?

Variables with nonlinear relationships can sometimes be transformed to be linear. Signup and view all the answers

What does a lurking variable cause in the correlation between two variables?

It causes a spurious correlation. Signup and view all the answers

What is the objective of linear regression according to the text?

To fit a straight line to the data. Signup and view all the answers

Which variable is referred to as the response in linear regression?

Output variable Signup and view all the answers

Why are linear relationships preferred over nonlinear ones in certain cases?

Nonlinear relationships can sometimes be closely approximated by linear relationships. Signup and view all the answers

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 Signup and view all the answers

Why is it challenging to determine the 'best-fitting' line using visual inspection?

Different people will perceive lines differently Signup and view all the answers

What does the least squares line minimize in the context of regression analysis?

Sum of squared deviations from the data Signup and view all the answers

How are the estimated values of β0 and β1 calculated using the least square method?

By minimizing the sum of squared errors Signup and view all the answers

What does yb represent in the context of a regression line with equation y = βb1x + βb0?

Predicted value given an x-variable Signup and view all the answers

Why do we use scatter diagrams before estimating β0 and β1 for regression analysis?

To determine if a linear relationship exists between variables Signup and view all the answers