4. (15%) Let \( Y_1, Y_2, ..., Y_{11} \) be a random sample of size \( n = 11 \) from Group 1 with mean \( \mu_1 \) and variance \( \sigma_1^2 \); and their sample mean is \( \bar{Y}_1 \) and sample variance is \( S_1^2 = \left( \sum_{i=1}^{11} (Y_i - \bar{Y}_1)^2 \right) / (n-1) \). Let \( Y_{12}, Y_{13}, ..., Y_{24} \) be the other random sample of size \( m = 13 \) from Group 2 with population mean \( \mu_2 \) and variance \( \sigma_2^2 \); and their sample mean is \( \bar{Y}_2 \) and sample variance is \( S_2^2 = \left( \sum_{i=12}^{24} (Y_i - \bar{Y}_2)^2 \right) / (m-1) \). Let \( D_i \) be a dummy, whose value is 1 if \( Y_i \) from Group 1, and is 0 if \( Y_i \) from Group 2, \( i = 1, 2, ..., 24 \). A simple regression is estimated as follows: \[ \hat{Y}_i = 1.66 - 0.63D_i \] whose \( \text{SSE} = \sum_{i=1}^{24} (Y_i - \hat{Y}_i)^2 = 6.6 \).