How close is the Line of Best Fit One additional method to determine if a linear model is appropriate for a data set is to analyze the residuals Do this by comparing the actual data point to the predicted outcome using the equation ID: 1026950
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1. Residuals and Residual Plots
2. How close is the Line of Best Fit?One additional method to determine if a linear model is appropriate for a data set is to analyze the residuals.Do this by comparing the actual data point to the predicted outcome using the equationA residual is the vertical distance between an observed data value and its predicted value using the regression equation.A residual plot is a scatter plot of the independent variable on the x-axis and the residuals on the y-axis.Residual value = observed value – predicted valueThe Residual Value is the difference between the actual observed value and the value predicted by the equation
3. Use Residual Plots to Interpret DataThe shape of the residual plot can be useful to determine whether a linear model is a good fit for a data set or notLinear:If a residual plot results in no identifiable pattern or a flat pattern, then the data may be linearly related. This means most of the data points were about the same distance from the line of best fit so the line had a strong correlation to the data
4. Use Residual Plots to Interpret DataNon-Linear:If there is a pattern in the residual plot, the data may not be linearly related. (it could have some type of non-linear relationship like quadratic, exponential, or none at all)
5. Residuals Example –Follow Along in Carnegie Book Lesson 3 pg 198-200The table below shows data of the speed at which a car is travelling and the distance it takes to brake to a complete stop.
6. Residuals Example –Follow Along in Carnegie Book Lesson 3 pg 198-2001. Construct a scatterplot and line of best fit)2. Correlation coefficient r = .99, strong positive linear association3. The linear regression equation is y = 5.4x - 134
7. Residuals Example pg199Now calculate the residualsThe linear regression equation is y = 5.4x - 134Next, subtract: Residual value = observed value – predicted valueThe Residual Value is the difference between the actual observed value and the value predicted by the equationFirst, use the linear regression equation to calculate the predicted braking distance (y value / output) for each speed (x value / input)
8. Now Create a Residual Plot pg200The residual plot is a scatter plot of the independent variable on the x-axis and the residuals on the y-axis.It will show you how far away each actual data point is from the line of best fitTo Graph: keep the x axis the same (speed as the independent variable) and graph the residual value on the y axis