Arrange the steps involved in assessing model fitness (regression analysis) in the correct sequence:

A. Estimate the mean of residuals

B. Assessment of mean of fitted dependent variable and given dependent variable

C. Estimate the value of a and b from the equation y=a+bx

D. Assessment of the mean of the residuals

E. Calculate the value of residuals

Choose the most appropriate answer from the options given below:

Correct option is B

Introduction:

• Regression analysis is a powerful statistical method used to examine and quantify the relationship between a dependent variable (outcome) and one or more independent variables (predictors).
•  It is frequently used to model how specific factors (like temperature or pollutant concentration) influence biological or ecological responses.

Information Booster:

• To establish the correct sequence, we proceed according to the natural workflow of model construction followed by diagnostic verification in regression analysis.
• The process begins with  (Estimate the value of aaa and bbb). Before any evaluation is possible, the regression model must be specified by estimating the intercept (aaa) and slope (bbb) using a method such as Ordinary Least Squares (OLS), giving the fitted equation
• y=a+bxy = a + bxy=a+bx
• Once the model is defined, we move to  (Calculate the value of residuals). Residuals represent the deviation of observed values from model predictions and are computed for each observation as  $$e_i = y_i - \hat{y}_i$$​.
• After obtaining the individual residuals, (Estimate the mean of residuals) follows. Here, the residuals are aggregated to compute their average, which serves as an indicator of potential bias in the model.
• This leads naturally to (Assessment of the mean of the residuals). In a correctly specified linear regression model with an intercept, the mean of the residuals should be zero. Verifying this condition confirms the absence of systematic over- or under-estimation.
• Finally, (Assessment of the mean of the fitted and observed dependent variables) is performed. This involves comparing the mean of the predicted values  ($$\hat{y})$$with the mean of the observed values $$(\bar{y} = \bar{\hat{y}}).$$​​
• For an OLS regression with an intercept, these two means are equal, reinforcing the internal consistency of the fitted model.