# How can you apply to potentially-dependent variables to an average?

I'm attempting to estimate a person's annual spending on healthcare based on their household income and age.

Given the following data from the Consumer Expenditures Survey:

Healthcare Spending (Average)
$4,968  Healthcare Spending (by Household Income)$0–49K     $3,411$50–99K    $5,151$100–149K  $6,836$150–199K  $7,664$200+K     $9,031  Healthcare Spending (by Respondent Age) 0–24$1,206
25–44  $3,072 45–64$5,450
65+    $6,802  It seems fairly easy to do the following: • If I know a person's household income is $85,000 I can estimate their annual healthcare spending at $5,151. • If I know a person's age is 42 I can estimate their annual healthcare spending at $3,072.

But if I knew both of those facts, how would I go about estimate their spending using both breakdowns at once? Ensuring that I'm not accidentally "double counting" the impact if the two variables are not fully independent.

I also happen to know the average household incomes for each age group, and the average age for each income group.

Household Income (by Respondent Age)
0–24   $32,268 25–44$74,082
45–64  $98,538 65+$51,624

Respondent Age (by Household Income)
$0–49K 54.0$50–99K    48.6
$100–149K 47.9$150–199K  48.8
\$200+K     49.7


I figure those two will be involved to determine how co-dependent the two variables are. But I'm not sure how to detangle them.

It depends on a lot of different thing. How much data and what kind of data do you have? If you have a bunch of data points of the form (income, age, spending) then I suspect that a straightforward multiple linear regression should work. If you believe there are interaction terms, you can try adding some additional explanatory variables by transforming the data; e.g. map each (income, age, spending) to (income, age, income * age, spending), or even (income, age, income / age, spending).