Asked by Leonel Mazariegos on Sep 24, 2024
Verified
Which of the following is a property of the slope,b1?
A) The slope equals one if X and Y have the same variance.
B) The slope has the same sign as r,the coefficient of correlation.
C) The slope equals one if r equals one.
D) All of these choices are true.
Slope
A measure of the steepness or incline of a line, representing the ratio of the change in the y-value to the change in the x-value.
Coefficient of Correlation
A statistical measure that computes the strength and direction of a linear relationship between two variables.
- Acquire knowledge of the formulation and ramifications of slopes and intercepts in the context of linear regression.
Verified Answer
IS
Inderdeep Singh3 days ago
Final Answer :
B
Explanation :
The slope (b) of the regression line has the same sign as the coefficient of correlation (r), which means that if r is positive, the slope is also positive, and if r is negative, the slope is also negative. The other options are not always true: A) the slope equals the ratio of the standard deviations of Y and X, not their variances; C) the slope equals the correlation coefficient only if both the standard deviation of Y and the standard deviation of X are equal to 1.
Learning Objectives
- Acquire knowledge of the formulation and ramifications of slopes and intercepts in the context of linear regression.
Related questions
The Slope B 1 of the Least Squares Line Represents ...
The Y-Intercept,b 0 ,of the Least Squares Line Represents The ...
{Allman Brothers Concert Narrative} Interpret the Value of the Slope ...
{Oil Quality and Price Narrative} Plot the Least Squares Regression ...
A Researcher Studying the Relationship Between the Number of Hours ...