Question

1. Use any math/stat software (e.g., www.numbergenerator.org/randomnumbergenerator) of your choice to find a random number generator to randomly select 20 rows of Table B.5 of Textbook. Then perform a multiple regression fit to the data you generated. The multiple regression model contains the response variable y (CO2) and regressors x1 (space time in min) and x6 (solvent total) and intercept.

a) Construct a normal probability plot of the residuals. Does there seem to be any problem with the normality assumption?

b) Construct and interpret a plot of the residuals versus the predicted response.

c) Compute the studentized residuals and the R-student residuals for this model. What information is conveyed by these scaled residuals?

d) Compute all other residuals (e.g., PRESS) to examine whether there are some observations that may not fit the model or potential outliers.

Answer 1

To perform a multiple regression fit, select a random sample and construct a normal probability plot of the residuals. Then, construct and interpret a plot of the residuals versus the predicted response. Compute studentized and R-student residuals, and examine other residuals to identify outliers or observations that may not fit the model.

Step-by-step explanation:

1. To perform a multiple regression fit, you need to select a random sample of 20 rows from Table B.5 of the Textbook. You can use a math/stat software or an online random number generator to randomly select the rows.
2. Once you have the data, identify the response variable (y) and the regressors (x1 and x6). The intercept should also be included in the multiple regression model.
3. Construct a normal probability plot of the residuals to check the normality assumption. If the points on the plot deviate significantly from the straight line, it suggests a problem with the normality assumption.
4. Construct a plot of the residuals versus the predicted response to check for any patterns or trends. If the points on the plot show a systematic pattern, it indicates a problem with the regression model.
5. Compute the studentized residuals and the R-student residuals to assess the influence of individual observations on the multiple regression model.
6. Compute other residuals (e.g., PRESS) to examine whether there are any observations that may not fit the model or potential outliers.