Fitted values can also be known as fits. The fitted values represent point estimates of the average response for given predictor values. The values of predictors are also known as x-values. Keep on reading to learn about fit regression line and more.
What is a fitted regression line?
A fitted regression line on a graph represents of the mathematical regression equation for your data. Use fitted regression lines to illustrate the relationship between a predictor variable (x-scale) and a response variable (y-scale) and to evaluate whether the model fits your data.
The specific x-values of each observation are entered into the model equation to calculate the fitted values.
If the equation is y=5 + 10x, then the fit value for the xvalue, 2, would be 25 (25 + 5 + 10(2)).
It is possible that observations with fitted regression line values that differ from the observed value are unusual. Unusual predictor values could be influential. Minitab will determine if your data contain unusual or influential values. Your output will include the table of Fits and Diagnostics for Unusual Observations. This identifies these observations. Minitab labels don’t follow the regression equation very well, which is an unusual observation. It is normal to have some unexpected observations. Based on the criteria of large standardized residuals you can expect approximately 5% to be flagged for having large standardized residuals. Unusual observation has more information about unusual values.
SE Fit regression line
The standard error (SE fit) is a measure of variation in the expected mean response for the given variable settings. The standard error of fit is used to calculate the confidence interval for the average response. Standard errors are never negative.
Measure the average response
To measure the precision of an estimate of the average response, use the standard error in the fit. The predicted mean response will be more accurate if the standard error is smaller. An analyst might create a model that predicts delivery time. The model predicts that the average delivery time will take 3.80 days for a given set of variables. These settings have a standard error of 0.08 days. The model returns the same average delivery time for the second set of variables, with a 0.02-day standard error of fit. Analysts can be more certain that the average delivery time for the second set is within 3.80 days.
The fit regression line value can be used to calculate a confidence interval for calculating the mean response. A 95% confidence interval is, for example, approximately two standard errors below and above the predicted mean depending on how many degrees of freedom you have. The 95% confidence interval is 3.64 and 3.96, respectively, for delivery times. 95% confidence can be placed on the population mean is within this range. The 95% confidence interval for a standard error of 0.02 is (3.76, 3.84) days. Because the standard error for this second set of variables is lower, the confidence interval is shorter.
Estimate the fitted value
To estimate the estimated value of the fit regression line value for observed variables, use the confidence interval.
With a confidence level of 95%, for example, you can be 95% certain that the confidence interval includes the population mean for the values specified by the predictor variables. You can use the confidence interval to assess the practical significance and utility of your results. You can use your expertise to determine if the confidence interval contains values that are relevant to your situation. If the confidence interval is large, you may be less confident about future values. Consider increasing the sample size if you find the interval too large to be of any use.