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the two regression lines are given by: y=40/18×214/18and x=10/8y-66/8variamce=9 find correlation coefficient between x and y
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the two regression lines are given by: y=40/18×214/18and x=10/8y-66/8v...
To find the correlation coefficient between x and y, we first need to find the slope of the regression line for y on x and the slope of the regression line for x on y.
Slope of regression line for y on x:
y = (40/18)x + 214/18
y = 20/9x + 107/9
The slope is 20/9.
Slope of regression line for x on y:
x = (10/8)y - 66/8
x = 5/4y - 33/4
The slope is 5/4.
Next, we need to find the standard deviations of x and y:
From the variance, we know that the standard deviation of y is √(9) = 3.
Let's assume that the standard deviation of x is also 3.
Finally, we can use the formula for the correlation coefficient:
r = (slope of regression line for y on x) * (standard deviation of x) / (slope of regression line for x on y) * (standard deviation of y)
r = (20/9) * 3 / (5/4) * 3
r = 8/5
r = 1.6/1
The correlation coefficient between x and y is 1.6.
Slope of regression line for y on x:
y = (40/18)x + 214/18
y = 20/9x + 107/9
The slope is 20/9.
Slope of regression line for x on y:
x = (10/8)y - 66/8
x = 5/4y - 33/4
The slope is 5/4.
Next, we need to find the standard deviations of x and y:
From the variance, we know that the standard deviation of y is √(9) = 3.
Let's assume that the standard deviation of x is also 3.
Finally, we can use the formula for the correlation coefficient:
r = (slope of regression line for y on x) * (standard deviation of x) / (slope of regression line for x on y) * (standard deviation of y)
r = (20/9) * 3 / (5/4) * 3
r = 8/5
r = 1.6/1
The correlation coefficient between x and y is 1.6.
Community Answer
the two regression lines are given by: y=40/18×214/18and x=10/8y-66/8v...
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