Hypothesis: As getting older people are more likely to have fairly good or bad health.

So, note that this is an example where I recoded the following categories: 1-very good, 2-good, 3-fair, 4-bad, 5-very bad.

1 and 2 -> rather good health

3,4,5 -> rather fairly good or bad

weight off.
fre health.
RECODE health (1 2=0)(3 thru 5=1) into health_2cat.
VARIABLE LABELS health_2cat ‘Subjective general health’.
VALUE LABELS health_2cat 0’rather good’ 1’fair or rather bad’.
fre health health_2cat.

fre agea.

LOGISTIC REGRESSION health_2cat WITH agea.

1-rather fairly good or bad
0-rather good
Indep:age

b0: The logarithm of the odds for a person feeling rather bad or fairly good at the age of 0 is -4,608. (Mathematically we can calculate with this, but our database does not contain 0-year-old persons.)

b1: The logarithm of the odds for a person feeling rather bad or fairly good compared to a one year older person is higher by 0,084. (Note: We stepped exactly 1 unit: from 0 age to age 1 or from age 1 to age 2, etc).

Exp(b1): The odds of feeling rather bad or fairly good are multiplicated by 1,087 for each year of life. (For a 24-year-old person the odds for feeling bad or fairly good are 1.087 times as high as for a 23-year-old person. So, between every 1 unit, every 1 age the odds increase 1.087 times).

Exp(b0): The odds for a person feeling rather bad or fairly good at the age of 0 are 0,010.

Conclusion: The results support the hypothesis stating that “As getting older people are more likely to have fairly good or bad health”. We conclude this because the p-value (p=0,000) is lower than 0,05 and the value of the Exp(b1) shows us that the odds of feeling fairly good or bad for a one year older person are higher.

Questions:

  1. What are the odds for a person to feel bad or fairly good when she is 3 years old?
    Exp(b1)*Exp(b1)*Exp(b1)*Exp(b0)=1,087*1,087*1,087*0,010
    That is Exp(b1) on the power of 3 * Exp(b0)
  2. What are the odds for a person to feel bad or fairly good when she is 4 years old?
    Exp(b1)*Exp(b1)*Exp(b1)*Exp(b1)*Exp(b0)=1,087*1,087*1,087*1,087*0,010.
    That is Exp(b1) on the power of 4 * Exp(b0)
  3. What are the odds for a person to feel bad or fairly good when she is 23 years old?
    Exp(b1)*Exp(b1)*Exp(b1)*Exp(b1)*…*Exp(b0)=1,087*1,087*…*0,010.
    That is Exp(b1) on the power of 23 * Exp(b0)
  4. For a 35-year-old how many times as high or low are the odds of feeling bad as for a 15-year-old?
  5. The age difference is 35-15=20, so the answer is Exp(b1) on the power of 20 *Exp(b0).
  6. What are the odds for a person to feel bad or fairly good when she is 70 years old?
    Exp(b1)*Exp(b1)*Exp(b1)*Exp(b1)*…*Exp(b0)1,087*1,087*…*0,010
    That is Exp(b1) on the power of 70 * Exp(b0)
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