Question

An important assumption underlying inferences from a linear regression is that variance in the response variable is reasonably consistent across the range of an explanatory factor (otherwise known as homoscedasticity).A. True B. false

Answer 1

Answer:

A. True

Step-by-step explanation:

Linear regression is "an analysis that assesses whether one or more predictor variables explain the dependent (criterion) variable.  The regression has five key assumptions:

1) Linear relationship : We need to check if the dependnet variable present a linear relationshipThe linearity assumption can best be tested with scatter plots in order to check if we have outliers in the data.

2) Multivariate normality : "The linear regression analysis requires all variables to be multivariate normal".  And we can check this with a histogram or a Q-Q-Plot, usually Normality can be checked with a goodness of fit test like the Kolmogorov-Smirnov test or Shapiro Wilks test.

3) No or little multicollinearity : "Multicollinearity occurs when the independent variables are too highly correlated with each other". And we can check this with a correlation matrix, variance inflation factor (VIF's), correlation index and other statistics.

4) No auto-correlation : The "Autocorrelation happens when the residuals are not independent from each other in the data". And usually we can test this with the Durbin-Watson test.

5) Homoscedasticity: MEans that we need constant variance for the linear model. The scatter plot is good way to check whether the data are homoscedastic. And we can interpret this condition as "that variance in the response variable is reasonably consistent across the range of an explanatory factor (otherwise known as homoscedasticity)"

So then the statement is TRUE.