Calculating the line of best fit involves using the regression function on a graphing calculator to find the slope and y-intercept, and writing the equation in the form ý = a + bx. To find the correlation coefficient, refer to the value given after the regression analysis, indicating the strength of the linear relationship.
To answer the student's questions regarding the equation of the line of best fit and the value of the correlation coefficient for a given dataset, follow these steps:
Line of Best Fit
Enter the data into the graphing calculator.
Use the calculator's regression function to calculate the least-squares regression line. This process will provide you with the slope (b) and y-intercept (a) of the line.
Write the equation in the form ý = a + bx, where 'a' is the y-intercept and 'b' is the slope.
Add the regression line to the scatter plot on the calculator.
Correlation Coefficient
After calculation of the least-squares regression line, the calculator will also provide the correlation coefficient (r).
Interpret the significance of the correlation coefficient. A value close to 1 or -1 indicates a strong relationship, while a value close to 0 indicates a weak relationship.
If the scatter plot shows a linear relationship, and the correlation coefficient is significant, these measures will meaningfully summarize the data's trend.