### Linear Regression and Correlation CoefficientWhen performing a linear regression analysis, you typically generate a scatter plot using software like Excel. The next step is to plot the trend line and find the corresponding regression equation and $ r^2 $ value.In this example, Excel reports the regression equation as:\[ y = 96.35x + 77.69 \]Additionally, it provides the $ r^2 $ value:\[ r^2 = 0.36 \]To understand the strength and direction of the linear relationship between the variables, we need to calculate the correlation coefficient, denoted as $ r $.**Question: What is the correlation coefficient for this data set?**You can calculate the correlation coefficient by taking the square root of $ r^2 $. Since $ r^2 = 0.36 $, we compute $ r $ as follows:\[ r = \sqrt{0.36} \]Since $ r $ can be either positive or negative depending on the direction of the relationship:\[ r = \pm 0.6 \]So, the correlation coefficient for this data set can be $ +0.6 $ or $ -0.6 $, indicating a moderate positive or negative linear relationship, respectively. The actual sign of $ r $ would depend on the nature of the data and the slope of the regression line. Given that the slope of the regression equation $ 96.35 $ is positive, $ r $ would be $ +0.6 $.

Answered: Image /qna-images/answer/8535d76a-4c2c-4f5a-86a1-45efdf946257.jpg

You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r2 value. The regression equation is reported as y = 96.35z + 77.69 and the r2 = 0.36. What is the correlation coefficient for this data set?

You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r2 value. The regression equation is reported as y = 96.35z + 77.69 and the r2 = 0.36. What is the correlation coefficient for this data set?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y=−66.75x+57.0 and the r=−0.504. Report answer as a percentage accurate to one decimal place.
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as 90.18x + 67.52 and the r = -0.345. What proportion of the variation in y can be explained by the variation in the values of x? s2 = Report answer as a percentage accurate to one decimal place.
You generate a scatter plot. You then plot the regression line and report the equation and the r2 value. The regression equation is reported as y=−84.57x+32.01 the r2=0.3025What is the correlation coefficient for this data set? r =
I’m taking a statistics and probability class. Please get this correct because I want to learn. I have gotten wrong answers on here before
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = - 97.06x + 49.41 and the r = - 0.77. What percentage of the variation in y can be explained by the variation in the values of x? % (Report exact answer, and do not enter the % sign)
Refer to the Baseball 2018 data, which reports information on the 2018 Major League Baseball season. Let attendance be the dependent variable and total team salary be the independent variable. Determine the regression equation and answer the following questions. Click here for the Excel Data Filea-1. Draw a scatter diagram.1. On the graph below, use the point tool to plot the point corresponding to the Attendance and its team salary (Salary 1).2. Repeat the process for the remainder of the sample Salary 2, Salary 3, … ).3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y. a-2. From the diagram, does there seem to be a direct relationship between the two variables?multiple choice 1 Yes No b. What is the expected attendance for a team with a salary of $100.0 million? (Round your answer to 4 decimal places.) c. If the owners pay an additional $30 million, how many more people could they expect to attend? (Round your answer to 3…
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported asy=−71.07x+16.92y=-71.07x+16.92and the r=−0.52r=-0.52.What percentage of the variation in y can be explained by the variation in the values of x?r² = % (Report exact answer, and do not enter the % sign)
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported asy=20.41x+15.59y=20.41x+15.59and the r=0.272r=0.272.What proportion of the variation in y can be explained by the variation in the values of x?r² = %Report answer as a percentage accurate to one decimal place.
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported asy=−32.86x+33.54y=-32.86x+33.54and the r=−0.483r=-0.483.What proportion of the variation in y can be explained by the variation in the values of x?r² = %Report answer as a percentage accurate to one decimal place.
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = 30.42x + 81.82 and the r = 0.9. What percentage of the variation in y can be explained by the variation in the values of x? r2 = % (Report exact answer, and do not enter the % sign)
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported asy=−36.16x+83.35y=-36.16x+83.35and the r=−0.945r=-0.945.What proportion of the variation in y can be explained by the variation in the values of x?r² = %Report answer as a percentage accurate to one decimal place.
The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following is the best interpretation of the coefficient of determination r2? About 37% of the variation in arm span is accounted for by the linear relationship formed with the foot length. About 65% of the variation in foot length is accounted for by the linear relationship formed with the arm span. About 63% of the variation in arm span is accounted for by the linear relationship formed with the foot length. About 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.