![]() The linear regression below was performed on a data set with a TI calculator. According to the linear regression equation, what would be the approximate value of y when x = 3?.What is the correlation coefficient and the coefficient of determination? Is the linear regression equation a good fit for the data?.Remember, it is always important to plot a scatter diagram first. What is the linear regression equation? The graph of the line of best fit for the third-exam/final-exam example is as follows: The least squares regression line (best-fit line) for the third-exam/final-exam example has the equation: y 173.51 4.83x y 173.51 4.83 x.Use the information shown on the screen to answer the following questions: ![]() Which of the following calculations will create the line of best fit on the TI-83?.This means that the linear regression equation is a moderately good fit, but not a great fit, for the data. You can see that r, or the correlation coefficient, is equal to 0.9486321738, while r 2, or the coefficient of determination, is equal to 0.8999030012. After pressing ENTER to choose LinReg(ax b), press ENTER again, and you should see the following screen: In other words, to find the correlation coefficient and the coefficient of determination, after entering the data into your calculator, press STAT, go to the CALC menu, and choose LinReg(ax b). If the correlation coefficient is negative. The closer the correlation coefficient is to 1 or 1, the stronger the correlation. The correlation coefficient will have a value between 1 and 1. The correlation coefficient and the coefficient of determination for the linear regression equation are found the same way that the linear regression equation is found. A multiple regression analysis reveals the following: The multiple regression model is: Notice that the association between BMI and systolic blood pressure is smaller (0.58 versus 0.67) after adjustment for age, gender and treatment for hypertension. The calculator is also able to find the correlation coefficient (r) and the coefficient of determination (r 2 ) for the linear regression equation. Is the linear regression equation a good fit for the data? Recognize the distinction between a population regression line and the estimated regression line. Know how to obtain the estimates b 0 and b 1 from Minitab's fitted line plot and regression analysis output. Interpret the intercept b 0 and slope b 1 of an estimated regression equation. \)ĭetermining the Correlation Coefficient and the Coefficient of Determinationĭetermine the correlation coefficient and the coefficient of determination for the linear regression equation that you found in Example B. Understand the concept of the least squares criterion.
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