Question

One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.

A. True
B. False

Answer 1

The statement provided is TRUE.

Explanation:

The four principle assumptions of the simple linear regression model are,

• The linearity of the relationship between the dependent variable and the independent variable. That is, value of y, the dependent variable for each value of x the independent variable is,
  `y = \beta_(1) + \beta_(2)x + e`.
• Normality of the error distribution. That is,
  `e_(i) ~\sim N (\mu, \sigma^(2))`. Thus, the variance of random error e is
  `Var (e) = \sigma^(2)`.
• Statistical independence of the errors or specifically no correlation between consecutive errors. That is, if
  `Corr (e_(i), e_(j)) = 0`, it implies that
  `Cov (e_(i), e_(j)) = 0`.
• Homoscedasticity of the errors, i.e. constant variance.

The first assumption clearly indicates that the y-values are statistically dependent upon the x-values.

Thus, the statement provided is TRUE.