Question

Consider the excel regression above. What null hypothesis is the (default) F-test, which is reported on the results, testing? What is the calculated F-statistic value and what is the p-value of the test? How many numerator degrees of freedom (restrictions) are involved?

Regression Statistics MultipleR 0.267643168 0.071632865 R Square Adj R Square 0.068838449 Standard Error571.4177199 Observations 3000 ANOVA df Significance F MS 9 75330553.98 8370061.553 25.634287096.23834E-43 Regression Residual 2990976289449.8 326518.2106 Total 2999 1051620004 Coefficients Standard ErrortStat P-value Lower 95% Upper 95% 2,807 135.0862973 20.78654569 9.48377E-90 2543.105992 3072.848988 Intercept tri 1 previsit 572 106.3636348 5.3844881727.82774E-08364.1604175 781.26705 tri 2 previsit 534 108.1423789 4.943902709 8.07975E-07 322.6043975 746.6864021 tri 3 previsit 521 119.2551585 4.374769611 1.25718E-05 287.8833728 755.5443138 smoker 135.265497 2.491173451 0.012786027 71.74694988 602.1926802 336 unmarried -21929.10687781-7.554818602 5.54057E-14-276.9687167-162.8256471 educatiorn 4.6 5.6185517780.821165448 0.411617501 -6.402858088 15.63037926 1.5 2.483822317 0.597390522 0.550291916 -3.386361827 6.353985651 age smokerx age 20 5.173408809-3.907855423 9.51833E-05-30.36073484 -10.0731325 drinks 3.415.30754516 0.22503005 0.821971275-33.45904472 26.56972941 The dependent variable is the birthweight of a newborn baby in grams. The independent variables are:

Answer 1

Null hypothesis:

F test

Ho:$\beta i=0$

where i =1,2,3,4,5,6,7,8,9

or can also be written as

Ho:$\beta 1=\beta 2=\beta 3=\beta 4=\beta 5=\beta 6=\beta 7=\beta 8=\beta 9=0$

What is the calculated F-statistic value and what is the p-value of the test?

F=25.63428709=25.63(rounding to 2 decimals)

p=6.23834*10^-43=0.0000(rounding to 4 decimals)

p<0.05

Reject Ho.

How many numerator degrees of freedom (restrictions) are involved?

df=9