We first introduce the concept of correlation in the Section 2.5 notes.Consider a linear model of the relationship between two quantitative variables in which the slope coefficient is non-zero. Which of the following statements about the slope coefficient and the correlation r between the two variables is correct?Question 1Select one:a.The slope coefficient could be negative when the correlation coefficient is positiveb.The slope coefficient and the correlation coefficient should have the same sign (both positive, or both negative)c.The slope coefficient could be positive when the correlation coefficient is negatived.The correlation coefficient can only be a positive value (regardless of whether the slope is positive or negative)Clear my choice
Question
We first introduce the concept of correlation in the Section 2.5 notes.Consider a linear model of the relationship between two quantitative variables in which the slope coefficient is non-zero. Which of the following statements about the slope coefficient and the correlation r between the two variables is correct?Question 1Select one:a.The slope coefficient could be negative when the correlation coefficient is positiveb.The slope coefficient and the correlation coefficient should have the same sign (both positive, or both negative)c.The slope coefficient could be positive when the correlation coefficient is negatived.The correlation coefficient can only be a positive value (regardless of whether the slope is positive or negative)Clear my choice
Solution
The correct answer is b. The slope coefficient and the correlation coefficient should have the same sign (both positive, or both negative).
Here's why:
The slope coefficient in a linear regression model measures the rate of change in the dependent variable as the independent variable changes. The correlation coefficient (r), on the other hand, measures the strength and direction of the linear relationship between two variables.
If the correlation coefficient is positive, it means that as one variable increases, the other also increases, and vice versa. This would mean that the slope of the line in the linear regression model is also positive.
Similarly, if the correlation coefficient is negative, it means that as one variable increases, the other decreases, and vice versa. This would mean that the slope of the line in the linear regression model is also negative.
Therefore, the slope coefficient and the correlation coefficient should always have the same sign.
Similar Questions
When is the correlation coefficient equal to 0?(1 Point)a) When there is a strong positive linear relationship.b) When there is a strong negative linear relationship.c) When there is no linear relationship.d) When there is a curvilinear relationship.
Which of the following statements about the correlation coefficient is FALSE? It measures the strength and direction of a linear relationship. A value of 0 indicates no linear relationship. It can only take positive values. A value of -1 indicates a perfect negative linear relationship.
Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals – 0.30, A. the variance of X is negative. B. variable X is larger than variable Y. C. there is no correlation. D. the slope (b1) is negative.
Q.1. Define correlation.
Assertion (A) Broadly, there only two types of correlation i.e., positive and negative.Reason (R) The correlation is said to be positive when the variables move together in the same direction, the correlation is negative when they move in opposite directions.
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