HZAU MULTIVARIATE HOMEWORK #2 MULTIPLE AND STEPWISE LINEAR REGRESSION

Transcription

1 HZAU MULTIVARIATE HOMEWORK #2 MULTIPLE AND STEPWISE LINEAR REGRESSION Using the malt quality dataset on the class s Web page: 1. Determine the simple linear correlation of extract with the remaining variables. a. Which of the variables have a correlation with extract that is significantly different from zero. b. Would you consider the correlation of the variables identified in part a as having a strong or weak association with extract? Explain your answer. 2. Determine the partial correlation between extract and viscosity, while controlling for beta-glucan content. a. Report the partial correlation value. b. When controlling for beta-glucan content, would you consider the relationship between malt extract and viscosity to spurious? Explain your answer. 3. Develop a regression model to predict the percent malt extract using the remaining variables as the independent variables. a. What is the regression equation? b. What independent variables have regression coefficients significantly different from zero? c. What percent of the variation in extract is explained by your regression model? d. Would you consider the regression model to adequately explain the variation in extract? Explain your answer. 4. Using stepwise regression, develop a regression model that includes those independent variables that significantly contribute to explaining the variation in extract. a. What is the regression equation? b. What percent of the variation in extract is explained by your regression model? c. Would you consider the regression model to adequately explain the variation in extract? Explain your answer.

2 options pageno=1; data hmwk2; input Line $ Plump Protein Extract amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose; datalines;.. Insert malt quality data from class Web page.. ;; proc corr; var extract; with Plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose; title 'Correlation of Extract with Independent s Related to Quality'; run; Proc corr; var extract viscosity; partial betagluc; title 'Partial Correlation of Extract and Viscosity While Controlling Betaglucan content'; run; proc reg; model extract=plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose; title 'Multiple Regression of Extract with the Remaining Quality Traits'; run; proc stepwise; model extract=plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose; title 'Stepwise Regression of Extract with the Remaining Quality Traits'; run;

3 14 With s: 1 s: Extract Correlation of Extract with Independent s Related to Quality The CORR Procedure 12:28 Thursday, June 21, Plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose Simple Statistics N Mean Std Dev Sum Minimum Maximum Plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose Extract

4 Pearson Correlation Coefficients, N = 61 Prob > r under H0: Rho=0 Extract Plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose

5 Partial Correlation of Extract and Viscosity While Controlling Beta-glucan content The CORR Procedure 1 Partial s: Betagluc 2 s: Extract Viscosity 12:28 Thursday, June 21, Simple Statistics N Mean Std Dev Sum Minimum Maximum Betagluc Partial Variance Partial Std Dev Extract Viscosity Pearson Partial Correlation Coefficients, N = 61 Prob > r under H0: Partial Rho=0 Extract Viscosity Extract Viscosity

6 Number of Observations Read 61 Number of Observations Used 61 Source Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept Plump Protein amylase DP kolbach Solprot Color FAN Betagluc Viscosity Fructose Glucose Maltose Maltotriose

7 Stepwise Regression of Extract with the Remaining Quality Traits The STEPWISE Procedure Model: MODEL1 Dependent : Extract Number of Observations Read 61 Number of Observations Used 61 12:28 Thursday, June 21, Stepwise Selection: Step 1 Betagluc Entered: R-Square = and C(p) = Source Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model Error Corrected Total Parameter Estimate Standard Error Type II SS F Value Pr > F Intercept <.0001 Betagluc Bounds on condition number: 1, 1 Stepwise Selection: Step 2 Viscosity Entered: R-Square = and C(p) =

8 Source Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Parameter Estimate Standard Error Type II SS F Value Pr > F Intercept <.0001 Betagluc Viscosity Bounds on condition number: , Stepwise Selection: Step 3 DP Entered: R-Square = and C(p) = Source Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Parameter Estimate Standard Error Type II SS F Value Pr > F Intercept <.0001 DP Betagluc Viscosity Bounds on condition number: ,

9 Stepwise Regression of Extract with the Remaining Quality Traits The STEPWISE Procedure Model: MODEL1 Dependent : Extract Stepwise Selection: Step 3 12:28 Thursday, June 21, Stepwise Selection: Step 4 Protein Entered: R-Square = and C(p) = Source Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Parameter Estimate Standard Error Type II SS F Value Pr > F Intercept <.0001 Protein DP Betagluc Viscosity Bounds on condition number: , All variables left in the model are significant at the level. No other variable met the significance level for entry into the model.

10 Step Entered Removed Summary of Stepwise Selection Number Vars In Partial R-Square Model R-Square C(p) F Value Pr > F 1 Betagluc Viscosity DP Protein