A local health clinic sent fliers to its clients to encourag

A local health clinic sent fliers to its clients to encourage everyone, but especially older persons at high risk of complications, to get a flue shot in time for protection against an expected flu epidemic. In a pilot follow-up study, 160 clients were randomly selected and asked whether they actually received a flu shot. In addition, data was collected on their health awareness, which was combined into a health awareness index, for which higher values indicate greater awareness. The estimated logistic regression model is

a. The probability of receiving a flu shot is multiplied by 0.0473 for every 1 unit increase in health awareness index.
b. The probability of receiving a flu shot is multiplied by 1.048 for every 1 unit increase in health awareness index.     
c. The odds of receiving a flu shot are multiplied by 0.0473 for every 1 unit increase in health awareness index.
d. The odds of receiving a flu shot increase by 0.0473 for every 1 unit increase in health awareness index.
e. The odds of receiving a flu shot increase by 1.048 for every 1 unit increase in health awareness index.
f. The odds of receiving a flu shot are multiplied by 1.048 for every 1 unit increase health awareness index.
g. The probability of receiving a flu shot increases by 0.0473 for every 1 unit increase in health awareness index.
h. The probability of receiving a flu shot increases by 1.048 for every 1 unit increase in health awareness index.

B) What are the odds that a client receives a flu shot if their health awareness index is 85?


C) What is the estimated probability that a client receives a flu shot if their health awareness index is 85?


D) Estimate the health awareness index at which 49% of all clients receive a flu shot.


E) Estimate the health awareness index at which the odds of receiving a flu shot are 2 to 3.


E) The researchers wish to perform a hypothesis test to determine if there is age is a significant predictor in the logistic model. What hypotheses should they test?

F) The p-value for the hypothesis test specified in part E is 0.0011. Based on this, the best conclusion the researchers can make at the = 0.05 level is:
    Note: You only have one submission for this problem.

a. There is a relationship between health awareness index and whether a flu shot was received.
b. There is a logistic relationship between health awareness index and whether a flu shot was received.
c. There is not a relationship between health awareness index and whether a flu shot was received.
d. There is not a linear relationship between health awareness index and whether a flu shot was received.
e. There is a linear relationship between health awareness index and whether a flu shot was received.
f. There is not a logistic relationship between health awareness index and whether a flu shot was received.

Solution

A)
e. The odds of receiving a flu shot increase by 1.048 for every 1 unit increase in health awareness index.

B) odds = exp ( -2.309 + (0.0473*85) ) = 5.537261......

c) estimated probability that a client receives a flu shot if their health awareness index is 85

= 5.537261 / ( 1 + 5.537261) =  0.8470307......

d) ln ( 0.49 / 0.51) =  -2.309 + 0.0473*(health awareness index).....

i.e, health awareness index = 47.97........

e) e)  Ha: b1 0Ho: 1 = 0

f) a. There is a relationship between health awareness index and whether a flu shot was received.