State true or false: Statement: there is no difference between, E(y) = 0 + 1x and y = 0 + 1x + e , both are regression equations True False
Question
State true or false: Statement: there is no difference between, E(y) = 0 + 1x and y = 0 + 1x + e , both are regression equations True False
Solution
False. While both are related to regression analysis, they are not the same. E(y) = 0 + 1x is the population regression line, which is a theoretical line that describes how the response variable y changes as the predictor x changes. On the other hand, y = 0 + 1x + e is the sample regression line, which is estimated from the data and includes the error term e. The error term accounts for the variability in y that cannot be explained by the linear relationship with x.
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