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

Answer:

The statement provided is TRUE.

Step-by-step 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.