![]() ![]() The formula, for those unfamiliar with it, probably looks underwhelming – even more so given the fact that we already have the values for Y and X in our example. To give some context as to what they mean: Having said that, and now that we're not scared by the formula, we just need to figure out the a and b values. a is the intercept, in other words the value that we expect, on average, from a student that practices for one hour.One hour is the least amount of time we're going to accept into our example data set. b is the slope or coefficient, in other words the number of topics solved in a specific hour ( X). ![]() As we increase in hours ( X) spent studying, b increases more and more. The weird symbol sigma ( ∑) tells us to sum everything up: Now that we have the average we can expand our table to include the new results: Hours (X) When they have a - (macron) above them, it means we should use the average which we obtain by summing them all up and dividing by the total amount: X and Y are our positions from our earlier table. Note: When using an expression input calculator, like the one that's available in Ubuntu, -2² returns -4 instead of 4. Which is a graph that looks something like this: We now have a line that represents how many topics we expect to be solved for each hour of study Now we replace the X in our formula with each value that we have: Hours (X) Our final formula becomes: Y = -1.85 + 2.8*X We've already obtained all those other values, so we can substitute them and we get: Calculating "a"Īll that is left is a, for which the formula is ͞͞͞y = a + b ͞x. If we want to predict how many topics we expect a student to solve with 8 hours of study, we replace it in our formula:Īn in a graph we can see: The further it is in the future the least accuracy we should expect LimitationsĪlways bear in mind the limitations of a method. It doesn't take into account the complexity of the topics solved.This will hopefully help you avoid incorrect results.Īnd this method, like any other, has its limitations. It's impossible for someone to study 240 hours continuously or to solve more topics than those available.So if the data we have is from different starting points of a course, the predictions won't be accurate A topic covered at the start of the " Responsive Web Design Certification" will most likely take less time to learn and solve than doing one of the final projects. The value of the slope (4.3) indicates that for each hour of training, the job skill score increases, on average, by 4.3 points.Regardless, the method allows us to predict those values. The value of the y-intercept (130) indicates the average job skill score for an employee with no training. Usually, this relationship can be represented by the equation y = b 0 + b 1x, where b 0 is the y-intercept and b 1 is the slope.įor example, a company determines that job performance for employees in a production department can be predicted using the regression model y = 130 + 4.3x, where x is the hours of in-house training they receive (from 0 to 20) and y is their score on a job skills test. When x increases by 1, y neither increases or decreases. When x increases by 1, y decreases by 0.4. The greater the magnitude of the slope, the steeper the line and the greater the rate of change.īy examining the equation of a line, you quickly can discern its slope and y-intercept (where the line crosses the y-axis). The slope and the intercept define the linear relationship between two variables, and can be used to estimate an average rate of change. The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis.
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