Since a new regression equation with extra variables was fit to the same data, the value of the F test statistic will be calculated as follows. The value of SSR(full) is the sum of squares due to regression of the model with the extra variables, SSR(reduced) is the sum of squares due to regression for the original model, the number of extra terms refers to the number of extra variables in the new model, and MSE(full) is the mean square error of the model with the extra variables.\[ F = \frac{\text{SSE(reduced)} - \text{SSE(full)}}{\text{number of extra terms}} \div \text{MSE(full)} \]The original model was \( \hat{y} = 25.2 + 5.5x_1 \) and the new model is \( \hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3 \). The new model added terms \( x_2 \) and \( x_3 \), so there are \( \boxed{2} \) extra terms.Recall that the value of the SSE for the original (reduced) model was given to be 520, so we have\[ \text{SSE(reduced)} = \boxed{260} \]There are no graphs or diagrams in the image. You may need to use the appropriate technology to answer this question.In a regression analysis involving 27 observations, the following estimated regression equation was developed.\[\hat{y} = 25.2 + 5.5x_1\]For this estimated regression equation SST = 1,525 and SSE = 520.(a) At \(\alpha = 0.05\), test whether \(x_1\) is significant.(b) Suppose that variables \(x_2\) and \(x_3\) are added to the model and the following regression equation is obtained.\[\hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3\]For this estimated regression equation SST = 1,525 and SSE = 100.Use an F test and a 0.05 level of significance to determine whether \(x_2\) and \(x_3\) contribute significantly to the model.**Step 1**

Given that the SSE of the reduced model is given as 520 in the question.SSE(reduced) = 520a) Given that for reduced model: SST = 1525 and SSE = 520Then, treatment sum of squares (TSS) = SST - SSE = 1525 - 520 = 1005Number of observations (n) = 27 and number of parameters in reduced model (k) = 2Null hypothesis: x1 is not significant.Significance level = 0.05Alternative hypothesis: x1 is significant.Test statistic: t = P-value = Pr(t>6.951) = 0.0000 (from R software).Since the p-value < 0.05, we can conclude that x1 is significant.b) Null hypothesis: x2 and x3 do not significantly contribute.Alternative hypothesis: x2 and x3 significantly contribute to the model.Significance level = 0.05Given that SSE(full) = 100, MSE = SSE/(n-kfull), where kfull = 4 is the number of parameters in full model and n = 27 is the sample size.Test statistic: F = P-value = Pr(F>48.3) = 0.0000 (from R software).Since the p-value < 0.05, we can conclude that x2 and x3 significantly contribute to the model.R-codes:1> 2*pt(6.951, df=25, lower. Tail = FALSE) #P-value for t 2[1] 0.00000 3> pf(48.3, df1=2, df2=23, lower. Tail = FALSE) #P-value for F 4[1] 0.00000a) x1 is significant.b) x2 and x3 significantly contribute to the model.