Question

Census data was collected on the 50 states and Washington, D.C. We are interested in determining whether average lifespan (LIFE) is related to the ratio of males to females in percent (MALE), birth rate per 1,000 people (BIRTH), divorce rate per 1,000 people (DIVO), number of hospital beds per 100,000 people (BEDS), percentage of population 25 years or older having completed 16 years of school (EDUC) and per capita income (INCO).

(a) Fit the MLR model with LIFE (y) as the response variable, and MALE (x1), BIRTH (x2), DIVO (x3), BEDS (x4), EDUC (x5), and INCO (x6), as predictors.
(b) At level α =5%, conduct the F-test for the overall fit of the regression. Comment on the results.

Concerning (b), what is the H0 and H1 for the F-test in THIS case?(please use the above case to explain). What command in R can we use to find the value that 0.05 has to compare with?What can we conclude if that value < 0.05? (I didn't provide the data as I only want to know how to do it instead of the exact answer, you can just assume that is a variable A here)

Answer 1

I assume that you have already fitted the MLR model and it will look like as,

LIFE (y) = Intercet + b0* MALE (x1)+ b1* BIRTH (x2)+ b2*DIVO (x3)+b3* BEDS (x4)+b4*EDUC (x5)+b5*INCO (x6)

concerning B)

Following is the set of hypothesis you would need for F-test

H0: The fitted Model is good that is, model with no independent variables fits the data as well as your model.

That is all the coefficients are equal to 0

H1: The fitted Model is not good that is, your model fits the data better than the intercept-only model.

That is all the coefficients are not equal to 0

What command in R ?

lm(LIFE (y) ~ MALE + BIRTH+DIVO+ BEDS+EDUC+INCO, data = data)

gives you the complete output and there only you can get p-value,

Following is the screenshot for your reference,

Last line gives you p-value

If -p value is less than 0.05 then we can conclude that, We Reject H0 and conclude that

The fitted Model is not good that is, your model fits the data better than the intercept-only model.

That is all the coefficients are not equal to 0