If it was one or 100%, that means all of it could be explained. Variance in the y variable is explainable by the x variable. R-squared, you mightĪlready be familiar with, it says how much of the Least-squares regression line fits the data. Now this information right over here, it tells us how well our So this is the slope and this would be equal to 0.164. Increase in caffeine, how much does the time studying increase? Or you might recognize this as the slope of the least-squares regression line. And then the coefficient on the caffeine, this is, one way of thinking about, well for every incremental Tells us essentially what is the y-intercept here. Visualize or understand the line is what we get in this column. And the most valuable things here, if we really wanna help And then this is giving us information on that least-squares regression line. Minimize the square distance between the line and all of these points. And a least-squares regression line comes from trying to Least-squares regression line looks something like this. And so for each of those students, he sees how much caffeine they consumed and how much time they spent studying and plots them here. And Musa here, he randomly selects 20 students. And then our y-axis, or our vertical axis, that would be the, I would assume it's in hours. So our horizontal axis, or our x-axis, that would be our caffeine intake in milligrams. Least-squares regression line? So if you feel inspired, pause the video and see if you can have a go at it. What is the 95% confidence interval for the slope of the Assume that all conditionsįor inference have been met. Here is a computer output from a least-squares regressionĪnalysis on his sample. Intake in milligrams and the amount of time Students at his school and records their caffeine \Interested in the relationship between hours spent studyingĪnd caffeine consumption among students at his school. When calculating the z-score of a sample with known population standard deviation the formula to calculate the z-score is the difference of the sample mean minus the population mean, divided by the Standard Error of the Mean for a Population which is the population standard deviation divided by the square root of the sample size. \(\sigma = \) population standard deviation.When calculating the z-score of a single data point x the formula to calculate the z-score is the difference of the raw data score minus the population mean, divided by the population standard deviation. You can also copy and paste lines of data from spreadsheets or text documents. Enter values separated by commas or spaces. With the last method above enter a sample set of values. With the first method above, enter one or more data points separated by commas or spaces and the calculator will calculate the z-score for each data point provided from the same population. A sample that is used to calculate sample mean and sample size population mean and population standard deviation.Sample mean, sample size, population mean and population standard deviation.A raw data point, population mean and population standard deviation.This calculator can find the z-score given: You can also determine the percentage of the population that lies above or below any z-score using a z-score table. A negative z-score means it's lower than average. The z-score allows you to compare data from different samples because z-scores are in terms of standard deviations.Ī positive z-score means the data value is higher than average. When you calculate a z-score you are converting a raw data value to a standardized score on a standardized normal distribution. You can calculate a z-score for any raw data value on a normal distribution. The z-score is the number of standard deviations a data point is from the population mean.
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