The two regression lines become identical if the correlation coefficient is
Question
The two regression lines become identical if the correlation coefficient is
Solution
The two regression lines become identical if the correlation coefficient is either +1 or -1.
Here's the step by step explanation:
-
Regression lines are statistical calculations that can be used to predict the value of one variable based on the value of another.
-
The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.
-
If the correlation coefficient is +1, it means there is a perfect positive linear relationship between the two variables. In this case, the regression lines would be identical and slope upwards.
-
If the correlation coefficient is -1, it means there is a perfect negative linear relationship between the two variables. In this case, the regression lines would be identical and slope downwards.
-
In any other case (when the correlation coefficient is between -1 and +1), the two regression lines would not be identical. They would show some degree of positive or negative correlation, but not a perfect one.
Similar Questions
The two regression lines become identical if the correlation coefficient isans.
The two regression lines become identical if the correlation coefficient is ans. 0 ±1 2 none
Suppose the correlation between two variables (x, y) in a data set is determined to be r = 0.63, What must be true about the slope, b, of the least-squares line estimated for the same set of data? The slope b is always equal to the square of the correlation r. The slope will also be a value between −1 and 1. The slope will have the same sign as the correlation. The slope will have the opposite sign as the correlation
If two variables are uncorrelated then regression lines are(a) Parallel(b) Perpendicular(c) Coincident(d) Inclined at 45 0
What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? Both r and b always have values between −1 and 1. b is always larger than r. r is always larger than b. r and b have the same sign (+ or −). The slope b is always equal to the square of the correlation r.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.