Y-values Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover Y-values and links to relevant pages within the course.
Learn more about laboratory continuing education for medical technologists to earn CE credit for AMT, ASCP, NCA, and state license renewal and recertification. Or get information about laboratory safety and compliance courses that deliver cost-effective OSHA safety training and continuing education to your laboratory's employees.
| Calculating the Y-Intercept To find the y-intercept, calculate and , the average of the x- and y-values respectively. Then substitute these two values for x and y in the = b + a equation. Finally, solve for the unknown quantity a. Therefore, the complete relationship between glucose concentration and absorbance for the data is y = 0.002x, where y is the absorbance and x is the glucose concentration. | View Page |
| The Least Squares Line According the the method of least squares, the line of best fit is the one that minimizes the squares of the differences between the data points' observed (experimental) y-values and their expected (theoretical) y-values. This line is known as the least squares regression line. To calculate the sum of squares of a line, find the difference between and the true y value for each point. is found by substituting the corresponding x value into the linear regression equation. Then square those differences, and then sum them. Line A is done below: Point x y Difference y- Difference Squared (y-)2 1 10 5.0 8.0 -3.0 9.00 2 18 24 14.4 9.6 92.16 3 38 27.5 30.4 -2.9 8.41 4 50 60.0 40.0 20.0 400.00 5 63 50.0 48.0 2.0 4.00 The total sum of squares for this line is 513.57. As said before, the line that minimizes this value is the line of best fit according to the least squares method. | View Page |
| Standard Error of Estimate The sum of squares of the deviations can also be used to provide an estimate of how closely the data cluster around the line. The Standard Error of Estimate (Se) is one such estimate, and is calculated according to the following formula, where S denotes summation, and the yi and i are the observed and theoretical y-values of the datapoints, respectively: For example, the Standard Error of Estimate of the preceding example is the following: | View Page |
| Confidence Intervals for Slope and Intercept Parameters In the last section, we calculated the best fit line for a sample of data. However, these data are subject to random sampling error, meaning that someone else could come later, perform the same experiment (x-values), and get different experimental results (y-values). Therefore, our data are random variables, and the slope and y-intercept we calculate using those data are also random variables, chosen from distributions around the true (population) slope and y-intercept. The true relationship between x and y is written y = b x + a. How close are the random variables a and b to the population parameters b and a? | View Page |