Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page. f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model. (Calculate an F statistic, obtain a tabled F value, and report the conclusion of your test, use a = .05). **Results for the Best Subsets Regression Analysis**This analysis presents the outcomes of various regression models used to identify the best subsets of explanatory variables for predicting the dependent variable \( y \). The analysis uses the R-Square Selection Method, detailing several statistical measures for each model:- **Model**: Number of variables included.- **R-Square**: Proportion of variance in \( y \) explained by the model.- **C(p)**: Mallow's C statistic, a criterion for model selection.- **MSE**: Mean Squared Error.- **BIC**: Bayesian Information Criterion.- **Variables in Model**: Specific predictor variables used.### Detailed Results:#### Model 1 (Single Variable Models)1. R-Square: 0.5259, Variables: x4 - R-Square: 0.4414, Variables: x3 - R-Square: 0.3447, Variables: x2 - R-Square: 0.1257, Variables: x1#### Model 2 (Two Variable Models)- R-Square: 0.8049, Variables: x2, x3- R-Square: 0.6847, Variables: x3, x4- R-Square: 0.6521, Variables: x1, x3- R-Square: 0.6440, Variables: x2, x4#### Model 3 (Three Variable Models)- R-Square: 0.9712, Variables: x1, x2, x3- R-Square: 0.8758, Variables: x2, x3, x4- R-Square: 0.7215, Variables: x1, x2, x4- R-Square: 0.6449, Variables: x1, x2, x4#### Model 4 (Four Variable Model)- R-Square: 0.9712, Variables: x1, x2, x3, x4---**Summary of SSR and SSE for Various Models:**- **Terms in Model**: Indicates the predictor variables included.- **SSR (Sum of Squares for Regression)**: Measures variation explained by the model.- **SSE (Sum of Squares for Error or Residuals)**: Measures unexplained variation.| Terms

Given that data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analysis of the data is provided.We are asked to perform a hypothesis test using the regression sum of squares information.To test for the full model H0: b2 = b4 = 0, we will use the full model with all 4 predictors and the model with only 1st and 3rd predictors.DF _numerator = k = number of predictors in full model - number of predictors in reduced model = 4-2 = 2DF _denominator = n = DF Residual for full model = 49Test statistic (F): F = 271.8364Given alpha (a) = 0.05Critical/tabled value = 3.1866 (from R software).Decision:Since the test statistic is greater than the critical value, we reject H0 and conclude that b2 and b4 are jointly significant.R-codes:1> qf(0.05, 2, 49, lower.tail = F) #critical value 2[1] 3.1866Reject H0 at a 5% level of significance. b2 and b4 are jointly significant