a. What are the sample estimates of β0,β1,and β2?b. What is the least squares prediction equation?c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem.d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01.e. Use a 95% confidence interval to estimate β2.f. Find R2 and R^2_a and interpret these values.g. Find the test statistic for testing H0: β1=β2=0.h. Find the observed significance level of the test in part g.interpret the result. ## Linear Regression Analysis Summary### Data TableA statistical software was used to fit the model \( E(y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 \) to \( n = 20 \) data points.### Regression EquationThe regression equation is:\[ Y = 1162.59 - 358.28x_1 - 94.31x_2 \]### Coefficients| Predictor | Coef | SE Coef | T | P ||-----------|-------|---------|------|------|| Constant | 1162.59 | 139.58 | 8.33 | 0.000 || X1 | -358.28 | 93.43 | -3.83 | 0.001 || X2 | -94.31 | 107.11 | -0.88 | 0.392 |### Model Statistics- **S**: 151.799- **R-sq**: 53.0%- **R-sq (adj)**: 47.0%### Analysis of Variance| Source | DF | SS | MS | F | P ||--------------|----|---------|--------|------|------|| Regression | 2 | 438,208 | 219,104| 9.51 | 0.002 || Residual Error | 17 | 391,731 | 23,043 | | || Total | 19 | 829,939 | | | |### Explanation of Terms- **Predictor**: The independent variables in the regression model (X1, X2).- **Coef**: The coefficients of the regression equation.- **SE Coef**: The standard error of the coefficients.- **T**: The t-statistic for the hypothesis test.- **P**: The p-value for the hypothesis test.- **S**: The standard deviation of the error term (residual standard deviation).- **R-sq**: The coefficient of determination, representing the percentage of the variance in the dependent variable that is predictable from the independent variables.- **R-sq (adj)**: The adjusted coefficient of determination, which adjusts for the number of predictors in the model

Name: a. What are the sample estimates of β0,β1,and β2?b. What is the lea
Uploaded: 2024-03-20T07:07:12.000Z
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Description: a. What are the sample estimates of β0,β1,and β2?b. What is the least squares prediction equation?c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem.d. Test H0: β1=0 against Ha: β1≠0.Use α=0.0