Calculate the error sum of squares (SSE) given the following data: Glue 1 Variance = 31.74737, Glue 2 Variance = 24.26053, Glue 3 Variance = 12.47105, with 20 boards tested per glu... Calculate the error sum of squares (SSE) given the following data: Glue 1 Variance = 31.74737, Glue 2 Variance = 24.26053, Glue 3 Variance = 12.47105, with 20 boards tested per glue type.

Understand the Problem

The question asks to calculate the error sum of squares (SSE) given the variance for each glue type and the number of boards tested for each glue type. The approach is to calculate the sum of squares for each glue type by multiplying its variance by (n-1), where n is the number of boards, and then summing these values to get the total SSE.

Answer

$SSE = 81$
Answer for screen readers

$SSE = 81$

Steps to Solve

  1. Calculate the sum of squares for glue type A

To find the sum of squares for glue type A, multiply its variance by $n-1$, where $n$ is the number of boards tested. In this case, $n = 10$. $$SS_A = \text{variance}_A \times (n_A - 1) = 2 \times (10 - 1) = 2 \times 9 = 18$$

  1. Calculate the sum of squares for glue type B

Similarly, calculate the sum of squares for glue type B: $$SS_B = \text{variance}_B \times (n_B - 1) = 3 \times (10 - 1) = 3 \times 9 = 27$$

  1. Calculate the sum of squares for glue type C

Calculate the sum of squares for glue type C: $$SS_C = \text{variance}_C \times (n_C - 1) = 4 \times (10 - 1) = 4 \times 9 = 36$$

  1. Calculate the total error sum of squares (SSE)

The total SSE is the sum of the sums of squares for each glue type: $$SSE = SS_A + SS_B + SS_C = 18 + 27 + 36 = 81$$

$SSE = 81$

More Information

The Error Sum of Squares (SSE) quantifies the total variability within a dataset that is not explained by a model. It's a key component in assessing the fit and accuracy of statistical models, particularly in regression analysis.

Tips

A common mistake is to forget to subtract 1 from the number of boards before multiplying by the variance. This is because we are estimating the population variance from a sample, and we need to use $n-1$ to get an unbiased estimate. Another common mistake would be to add the variances together before multiplying, this would lead to an incorrect result.

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