Y-intercept Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover Y-intercept and links to relevant pages within the course.
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| In a linear equation of the form y = bx + a, where x is the independent variable and y is the dependent variable, what are b and a? | View Page |
| Which of the following conditions will characterize a line with negative slope? | View Page |
| What are the slope and y-intercept for these data points?
x
y
15
2
20
6
30
14
40
22
50
30
| View Page |
| What are slope and y-intercept for this data? xyx-y-(x-)(y-)(x-)2 20 45 66 89 Recall: and | View Page |
| 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 |
| Determining the Least Squares Line Least squares would be a tedious process if we had to draw four of five lines of best fit and then determine which line had the least sum of squares, and then we still would have no way of knowing whether the line we had chosen was truly the best out of all possible lines. Consider the data in the following figure. The least squares formulae automatically provided the slope and y-intercept where the sum of squares (and therefore the Standard Error of Estimate) is smallest. | 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 |
| What are the slope and y-intercept of the least squares regression line for this data? | 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 |