In: Statistics and Probability
You have a sample of individuals and regress house price on the house size. You wish to (1) predict the actual price of a house that is 2,500 square feet in size and (2) predict the conditional mean price of a house that is 2,500 square feet. Then
The same predicted value is used for both (1) and (2) though the standard errors for purposes (1) and (2) will differ
The same predicted value is used for both (1) and (2) and the standard errors for purposes (1) and (2) will be the same
Different predicted values are used for (1) and (2) and the standard errors for purposes (1) and (2) will differ
Different predicted values are used for (1) and (2) though the standard errors for purposes (1) and (2) will be the same
Different predicted values are used for (1) and (2) though the standard errors for purposes (1) and (2) will be the differ.
If someone build a regression model , he\she may get a linear or non -linear equation between house price and house size.Now if he\she predict house price based on house price by using fitted model, he\she may get different values of house price for different models(for example house price value may be diifenent for cubic, quadratic and linear model).
Now if you want conditional mean of a house that is n square feet, We have to filter and note down all house price which are n square feet in size and calculate mean value of price of houses which are n square feet in size.
the standard errors for purposes (1) and (2) may be different. If sum of of square of residual (=actual value - predicted value)values are different for two purposes, then standard errors will be different.