2. Derive the sum of squares decomposition for the two-factor model with interaction.
Which of these is not related to the model sum of squares? a. The variance explained by the first predictor/independent variable b. The variance explained by the second predictor/independent variable c. The variance explained by the main effect of the two predictors/independent variables on each other d. The variance explained by the interaction of the two predictors/independent variables on each other
3. Consider the partially completed two-way ANOVA summary table. Source Sum of Squares Degrees of Freedom Mean Sum of Squares Factor B Factor A 600 200 Interaction 144 Error 384 Total 1,288 23 The number of Factor A populations being compared for this ANOVA procedure is _ A) 5 B) 7 C) 4 D) 6
3. Consider the two-factor model with interaction Suppose that there are a and b levels of the factors respectively. Now consider the set of equations (a) Show that the equations are not redundant. (b) Show that these equations are equivalent to the hypothesis of no interaction. (c) Thereby calculate the rank of the hypothesis of no interaction. (d) Show that the hypothesis is testable, provided there exists at least one sample from each combination of factor levels.
A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data. Factor B Level 1 Level 2 Level 3 135 90 75 Level 1 165 93 Factor A 135 127 120 Level 2 85 105 136 Test for any significant main effects and any interaction. Use α-.05. Round Sum of Squares, F value, Mean Square to two decimals, if necessary. Source of Variation Factor A Factor B Interaction Error Total Sum...
Derive the least squares normal equations for the model :
A sociologist classified 45 faculty members by subject matter of course (factor A with 4 levels) and highest degree earned (factor B with 3 levels) The first ANOVA table below is from a model including A and B main effects and AB interaction effects. The second one is from a model including B main effects and AB interaction effects but no A main effects Sequential sum of squares ANOVA table with A, B and AB terms. Analysis of Variance Source...
A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data. Factor B Level 1 Level 2 Level 3 125 100 65 Level 1 155 76 103 Factor A 105 147 140 Level 2 95 125 156 Test for any significant main effects and any interaction. Use . Round Sum of Squares, value, Mean Square to two decimals, if necessary and -value to four decimals. Source of Variation Sum of Squares Degrees...
CH13 Q8 A two-way analysis of variance experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. The results include the following sum of squares terms: SST 1548 SSA 1022 SSB 390 SSAB 26 a. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F' to 3 decimal places.) Answer is not complete. ANOVA...
Consider a factorial design model with 2 levels of Factor A, 3 levels of Factor B, and 2 observations at each combination of factor levels. Write this model in matrix notation as Y = X8+ €. Compute the matrices X'X and X'Y and use them to derive the least-squares estimators of all appropriate parameters from the normal equations XXB = X'Y Note: Do not write the matrices for a general factorial design model. Consider the particular factorial design described here.
Epidemiology In a hypothetical study investigating the interaction between factor A and factor B and the risk of disease X; Incidence of disease in the absence of factor A and factor B = 2 per 100,000 population Incidence of disease if factor A is present and factor B absent = 14 per 100,000 population Incidence of disease if factor B is present and factor A absent = 10 per 100,000 population 1. Using the additive model of interaction, what is...