Question

If x has a mean of 17.2 g and a standard division of 14.0 g and y has a mean of 23.5 g and a standard division of 16.4 g and they both have a correlation of 0.83. What is the LSRL

Answer 1

The least squares regression line is y=0.6831x+11.25

Step-by-step explanation:

LSRL is the the Least Squares Regression Line.The formula for regression line is y=mx+b where m is the slope of the line and b is the y-intercept value of the line.

First find the slope, m of the line from the means and standard deviations given

x has a mean of 17.2 g and a standard deviation of 14.0 g

y has a mean of 23.5 g and a standard deviation of 16.4 g

The correlation coefficient in both cases is 0.83, hence the slope m is given by;

m=r(Sy/Sx) where m is the slope of the line, Sy is standard deviation of y values, Sx  is standard deviation of x values and r is the correction coefficient.

m= 0.5 * 23.5/17.2 =0.6831

Find the value of b, the y-intercept

b=Y-mX where X and Y are the mean values for x and y respectively

b=23.5-0.6831*17.2

b=23.5-11.75=11.25

The LSRL is y=0.6831x+11.25

Learn More

Least Squares regression Line : brainly.com/question/4090838

Keyword : standard deviation, least square regression line

#LearnwithBrainly