Scatter Plot Generator
Least-Squares Regression Line, Residuals Plot and Histogram of Residuals To generate the residuals plot, click the red down arrow next to Linear Fit and. Creating an initial scatter plot. Before you can create a regression line, a graph must be produced from the data. What are the assumptions of Simple Linear Regression? The most useful graph for analyzing residuals is a residual by predicted plot. This is a graph of each.
This is a graph of each residual value plotted against the corresponding predicted value. If the assumptions are met, the residuals will be randomly scattered around the center line of zero, with no obvious pattern.
The residuals will look like an unstructured cloud of points, centered at zero. For example, if curvature is present in the residuals, then it is likely that there is curvature in the relationship between the response and the predictor that is not explained by our model.
A linear model does not adequately describe the relationship between the predictor and the response. In this example, the linear model systematically over-predicts some values the residuals are negativeand under-predict others the residuals are positive. This means that the variability in the response is changing as the predicted value increases.
Residual Analysis in Regression
This is a problem, in part, because the observations with larger errors will have more pull or influence on the fitted model. Outliers can have a big influence on the fit of the regression line.
In this example, we have one obvious outlier. Many of the residuals with lower predicted values are positive these are above the center line of zerowhereas many of the residuals for higher predicted values are negative. The one extreme outlier is essentially tilting the regression line. Using the linear equation labeled A in Figure 5a spreadsheet cell can have an equation associated with it to do the calculation for us. We have a value for y Absorbance and need to solve for x Concentration.
Residual Analysis in Regression
Below are the algebraic equations working out this calculation: The equation associated with the spreadsheet cell will look like what is labeled C in Figure 8. The solution for x Concentration is then displayed in cell 'C12'. Highlight a spreadsheet cell to hold 'x', the result of the final equation cell C12, labeled B in Figure 5. Click in the equation area labeled C, figure 5 Type an equal sign and then a parentheses Click in the cell representing 'y' in your equation cell B12 in Figure 5 to put this cell label in your equation Finish typing your equation Note: If your equation differs for the one in this example, use your equation Duplicate your equation for the other unknown.
Return to Top Using the R-squared coefficient calculation to estimate fit Double-click on the trendline, choose the Options tab in the Format Trendlines dialogue box, and check the Display r-squared value on chart box. Your graph should now look like Figure 6.
Note the value of R-squared on the graph. The closer to 1. That is, the closer the line passes through all of the points. Now lets look at another set of data done for this lab Figure 7.
Notice that the equation for the regression line is different than is was in Figure 6. The linear equation can be used to state the actual consumption of ice cream when we know the price of ice cream. The linear equation generates predictions for ice cream consumption where the sum of the squared residuals are minimized.
The linear equation suggests that when per capita consumption is at 0. Which statement best interprets the meaning of the slope of the prediction equation? For any two-variable data set, the calculator's cubic regression model will always generate a smaller SSE than will the calculator's linear regression model. A median-median line is to be generated from a scatter plot of data.Understanding Residual Plots
Given the scatter plot, what is the first step in creating the median-median line? Calculate the slope of the median-median line.