# Average value of y in linear regression

I've got a regression from the value of a house on things like x1 = number of bathrooms, x2 = number of bedrooms, x3 = age of the house and a couple more. I have the estimates of the coefficients belonging to those variables as well as their standard error, t-value, p-value and 95% CI.

Moreover, I got the number of observations, $R^2$, adjusted $R^2$ and the standard error of $y$.

Now I am supposed to calculate the average value of a house, which is the average value of $y$. But I got no idea how to calculate it with the information I have. Can anyone give me a hint?

• You're right: you can't calculate this from that information, because you need to know the full multivariate distribution of the explanatory variables. As an analogy, suppose you estimated that the height of a person (in meters) is 1/40 of their weight (in kilograms). What is the average height of people? The answer, of course, depends on which people. Someone could respond, "well, consider these data to be a random sample of the houses." In that case your best bet is to forget all about the regression and report the average of the house prices.
– whuber
Mar 8 '18 at 20:25
• I am a little confused. Did you do the regression yourself or you were only given information about the results of the regression? Mar 8 '18 at 20:32
• The results of the regression were given. it was a question from an exam last year, thats why I was so confused bc I expected that there has to be a solution
– F.V.
Mar 8 '18 at 20:48

When you know the solution of the regression $y=\alpha +\beta_1 x_1+\beta_2 x_2 + \epsilon$ then:
$$E(y)=\alpha +\beta_1 E(x_1)+\beta_2 E(x_2)$$
Obviously you need to known $E(x_1)$ and $E(x_2)$ to answer. Unless it is said somewhere that these variables were centred (in this case $E(y)=\alpha$), then there's nothing you can do.