Below is a computer output based on a sample of 506 observations with a few spots left blank

Below is a computer output based on a sample of 506 observations with a few spots left blank.

                                Coefficient          Standard Error   t-stat     p-value

Constant              -21.873                 3.178                     -6.883    1.76e-11                              

X₁                                          -0.099                    0.015                                     1.17e-10

X₂                            -0.480                    0.200                     -2.399    0.0168

X₃                            8.440                     0.410                     20.653   2e-16

ANOVA

Source of Variation         DF           Sum of Squares                Mean Square     F              p-value

Regression                          3              22878.8                                 193         2.2e-16

Error                                      502         19837.5 39.5

1. What is the estimated regression equation?
2. What is the interpretation of the coefficient of X₁?
3. What is the test statistic for whether β₁ is significant (calculate)?
4. Is the parameter β₁ significant at a 1% level (α=0.01)?
5. Is the parameter β₂ significant at a 1% level (α=0.01)?
6. What is the mean square regression (MSR)?
7. If you were to do a Backward Elimination based on the p-value of the t-statistic and an alpha to remove of 0.05, would you remove any variable in the first step and if so which one?