University:
University of Houston
Course:
MATH 2312 | Precalculus
Academic year:

2022
Views:

418

Pages:

11
Author:

Callboyx26e

5.4 - Residuals A residual value is the difference between an actual observed y value and the corresponding predicted y value. Residuals are just errors. Residual = error = (observed - predicted) = (y - ŷ) Example: A least-squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is ŷ = 16.6 + 0.65t where ŷ is the predicted weight and t is the age of the child. A 20-month old child in this group has an actual weight of 25 pounds. What is the residual weight, in pounds, for this child? Solution: ŷ(20) = 16.6 + 0.65(20) = 29.6 lbs residual = 25 - 29.6 = -4.6 lbs Popper 11 2. Association implies causation a. True b. False 3. If a correlation coefficient has a value of 0.9679, that means the data has a linear relationship and we do not have to look at the residual plot. a. True b. False 4. A residual plot with a pattern means a strong linear relationship a. True b. False 5. Choose E The plot of the residual values against the x values can tell us a lot about our LSRL model. Plots o residuals may display patterns that would give some idea about the appropriateness of the model. If the functional form of the regression model is incorrect, the residual plots constructed by using the model will often display a pattern. The pattern can then be used to propose a more appropriate model. When a residual plot shows no pattern, it indicates that the proposed model is a reasonable fit to a set of data. Here are some examples of residual plots that show patterns: Sum of all residuals should be 0 A data set produced the regression equation ŷ = 17.3 - .96x. Below are four of the data points. (This is a subset of entire set) x y ŷ res. 2 15 15.38 -0.38 11 7 10.58 -3.58 12 4 13.46 -9.46 5 12 5.78 6.22 5.78 <- plug x into ŷ Popper 11 What is the residual for the point (1, 2) given ŷ = 2.75 - 1.06x? a. -0.31 b. 0.31 c. 1.69 d. -1.69 e. none of these