X-values Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover X-values and links to relevant pages within the course.
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| Prediction Using the Resulting Equation Once the parameters have been calculated, the resulting equation can be used to make predictions about a value of y given a value of x, provided that the x value is in the same range of x-values that were used to derive the equation. For example, if x = 350 mg/dL, what is the expected value of y? To find the answer, substitute the known value of x into the equation.
When the concentration is 350 mg/dL, we expect the absorbance to be about 0.7. | View Page |
| Formulae for Determining the Slope and Intercept To find the slope, calculate the deviation of each x from mean, , and calculate the deviation of each y from its mean, . The numerator is the product of the deviation of each x and y pair, the denominator is the sum of the squared deviations of all of the x-values. Thus the formula is: The y-intercept, a, is calculated by substituting and into the equation of a line and solving for a: To draw this line on a graph, substitute two or three values for x, calculate the corresponding y values, plot these x-y pairs as points on the graph, and draw a line through these points. | 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 |