- #HOW TO FIND SIMPLE LINEAR REGRESSION EQUATION IN EXCEL HOW TO#
- #HOW TO FIND SIMPLE LINEAR REGRESSION EQUATION IN EXCEL SOFTWARE#
#HOW TO FIND SIMPLE LINEAR REGRESSION EQUATION IN EXCEL HOW TO#
Elsewhere on this site, we show how to compute the margin of error. We are working with a 99% confidence level. In this analysis, the confidence level is defined for us in the problem. From the regression output, we see that the slope coefficient is 0.55. Since we are trying to estimate the slope of the true regression line, we use the regression coefficient for home size (i.e., the sample estimate of slope) as the sample statistic. Use the following four-step approach to construct a confidence interval. What is the 99% confidence interval for the slope of the regression line? Regression equation:Īnnual bill = 0.55 * Home size + 15PredictorCoefSE CoefTPConstant1535.00.00Home size0.550.242.290.01 Output from a regression analysis appears below. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). The local utility company surveys 101 randomly selected customers. Note that this approach is used for simple linear regression (one independent variable and one dependent variable).
In the next section, we work through a problem that shows how to use this approach to construct a confidence interval for the slope of a regression line. And the uncertainty is denoted by the confidence level. The range of the confidence interval is defined by the sample statistic + margin of error. When calculating the margin of error for a regression slope, use a t score for the critical value, with degrees of freedom (DF) equal to n - 2. Previously, we showed how to compute the margin of error, based on the critical value and standard error. Often, researchers choose 90%, 95%, or 99% confidence levels but any percentage can be used. The confidence level describes the uncertainty of a sampling method. In the table above, the regression slope is 35. The sample statistic is the regression slope b1 calculated from sample data. Note, however, that the critical value is based on a t score with n - 2 degrees of freedom. The confidence interval for the slope of a simple linear regression equation uses the same general approach. Previously, we described how to construct confidence intervals. How to Find the Confidence Interval for the Slope of a Regression Line Where yi is the value of the dependent variable for observation i, ŷi is estimated value of the dependent variable for observation i, xi is the observed value of the independent variable for observation i, x is the mean of the independent variable, and n is the number of observations. If you need to calculate the standard error of the slope (SE) by hand, use the following formula: It might be "StDev", "SE", "Std Dev", or something else.
#HOW TO FIND SIMPLE LINEAR REGRESSION EQUATION IN EXCEL SOFTWARE#
However, other software packages might use a different label for the standard error.
In this example, the standard error is referred to as "SE Coeff".
In the output above, the standard error of the slope (shaded in gray) is equal to 20. The table below shows hypothetical output for the following regression equation: y = 76 + 35x. Many statistical software packages and some graphing calculators provide the standard error of the slope as a regression analysis output. To construct a confidence interval for the slope of the regression line, we need to know the standard error of the sampling distribution of the slope. Previously, we described how to verify that regression requirements are met. The approach described in this lesson is valid whenever the standard requirements for simple linear regression are met. Where b0 is a constant, b1 is the slope (also called the regression coefficient), x is the value of the independent variable, and ŷ is the predicted value of the dependent variable. We focus on the equation for simple linear regression, which is: This lesson describes how to construct a confidence interval around the slope of a regression line.