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Nick Stauner
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Say I have some data on people where I have a measure of their general health (some score out of 1000), the number of apples they eat in a year, and the number of oranges they eat in a year.

Then I do a multiple regression and I get something like:

Yhat = 442.22 + 1.1a + 0.7o$\hat Y = 442.22 + 1.1a + 0.7o$

where a$a$ is the apple variable, and o$o$ is the orange variable.

Is it legitimate for me to then say to someone who eats 1 apple and 1 orange a year, "Your predicted health score is 442.22 + 1.1 + 0.7 = 444.02$442.22 + 1.1 + 0.7 = 444.02$?"

I've been taught that I can only say things like "for each extra apple you eat your health is predicted to increase by 1.1 points, holding constant scores on the other variables". Did my interpretation in the previous paragraph violate this "holding constant" rule?

Say I have some data on people where I have a measure of their general health (some score out of 1000), the number of apples they eat in a year, and the number of oranges they eat in a year.

Then I do a multiple regression and I get something like

Yhat = 442.22 + 1.1a + 0.7o

where a is the apple variable, and o is the orange variable.

Is it legitimate for me to then say to someone who eats 1 apple and 1 orange a year "Your predicted health score is 442.22 + 1.1 + 0.7 = 444.02?"

I've been taught that I can only say things like "for each extra apple you eat your health is predicted to increase by 1.1 points, holding constant scores on the other variables". Did my interpretation in the previous paragraph violate this "holding constant" rule?

Say I have some data on people where I have a measure of their general health (some score out of 1000), the number of apples they eat in a year, and the number of oranges they eat in a year.

Then I do a multiple regression and I get something like:

$\hat Y = 442.22 + 1.1a + 0.7o$

where $a$ is the apple variable, and $o$ is the orange variable.

Is it legitimate for me to then say to someone who eats 1 apple and 1 orange a year, "Your predicted health score is $442.22 + 1.1 + 0.7 = 444.02$?"

I've been taught that I can only say things like "for each extra apple you eat your health is predicted to increase by 1.1 points, holding constant scores on the other variables". Did my interpretation in the previous paragraph violate this "holding constant" rule?

Is this the correct way to interpret regression coefficients?

Say I have some data on people where I have a measure of their general health (some score out of 1000), the number of apples they eat in a year, and the number of oranges they eat in a year.

Then I do a multiple regression and I get something like

Yhat = 442.22 + 1.1a + 0.7o

where a is the apple variable, and o is the orange variable.

Is it legitimate for me to then say to someone who eats 1 apple and 1 orange a year "Your predicted health score is 442.22 + 1.1 + 0.7 = 444.02?"

I've been taught that I can only say things like "for each extra apple you eat your health is predicted to increase by 1.1 points, holding constant scores on the other variables". Did my interpretation in the previous paragraph violate this "holding constant" rule?