A.12 ci for regression
- 1. Confidence Interval for the slope of a least-squares Regression Line
- 2. Equation for simple linear regression What is linear Regression? The least squares linear regression is a method for predicting the value of a dependent variable y, based on a value of the independent variably x. Equation: y*= a + bx Where: y*= predicted value of the dependent variable a= constant b= slope (regression coefficient) x= value of independent variable
- 3. Estimation Requirements • Dependent variable y has a linear relationship to the independent variable x. • For each value of x, the probability distribution of y has the same standard deviation • For any given value of x, – y values are independent – y values are approximately normally distributed
- 4. Properties of a Regression Line • With the regression parameters defined before for bo and b1 • The line minimizes the sum of the squared differences between the observed values )y-values) and the predicted values(y* values computed by the regression equation) • The regression line passes through the mean of the x-values (x) and through the mean of the y values (y) • Regression constant (b0) is equal to y-intercept of regression line • Regression coefficient (b1) is the average change in the dependent variable (y) for a 1-unit change in the independent variable (x). It is the slope of the regression line • The least squares regression line is the only straight line that has all of these properties
- 5. Standard Error The measure of the average amount that the regression equation over or under predicts. The higher the coefficient of determination, the lower the standard error and the more accurate predictions are likely to be. (this will always be given to you) Variability of Slope Estimate: Calculator provides standard error of slope as regression analysis output
- 6. How to find the Confidence Interval for the slope of a regression line Same approach as previous confidence intervals, BUT the critical value is based on a t-score with the degree of freedom as n-2. 1- sample statistic regression slope b, calculated from sample data 2- confidence level 3- Margin of Error 4- Confidence Interval: sample statistic + ME written as: (Sample Stat – ME, Sample Stat + ME)
- 7. How to find the Confidence Interval for the slope of a regression line Same approach as previous confidence intervals, BUT the critical value is based on a t-score with the degree of freedom as n-2. 1- sample statistic regression slope b, calculated from sample data 2- confidence level 3- Margin of Error 4- Confidence Interval: sample statistic + ME written as: (Sample Stat – ME, Sample Stat + ME)