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 have the same sign as the correlation. The slope will also be a value between −1 and 1. The slope will have the opposite sign as the correlation.
Question
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 have the same sign as the correlation. The slope will also be a value between −1 and 1. The slope will have the opposite sign as the correlation.
Solution 1
The slope, b, of the least-squares line estimated for the same set of data is not always equal to the square of the correlation, r. The slope may or may not have the same sign as the correlation. The slope is not necessarily a value between −1 and 1. The slope may or may not have the opposite sign as the correlation.
Solution 2
The slope, b, of the least-squares line estimated for the same set of data is not always equal to the square of the correlation, r. The slope may or may not have the same sign as the correlation. The slope is not necessarily a value between −1 and 1. The slope may or may not have the opposite sign as the correlation.
Similar Questions
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.
What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x
The two regression lines become identical if the correlation coefficient is
For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223.Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.Slope = 0.35y-intercept = 10.93Slope = 0.14y-intercept = 6.27Slope = 0.35y-intercept = 3.37Slope = 0.14y-intercept = 12.65
With Show least-squares fit line still selected, set r to 0.90. The points should be close tothe line, but not right on it. Below Generate new data set with: click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?A positive r indicates a positive correlation: as x increases, y also tends to increase.D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease.
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