Which Diagnostic Test Allows The Researcher To Claim That He

Which Diagnostic Test Allows The Researcher To Claim That Her Model

Identify the correct diagnostic test that enables a researcher to claim that her model explains a specific percentage of the variation in the dependent variable. The options include the Durbin-Watson test, Coefficient of Determination, t-test on the slope coefficient, Sum of squared residuals, or None of the above.

Determine which statement about a company's seasonal index for quarterly sales is incorrect. Options describe the sum of index numbers, interpretations of specific index values, the range of the index, and the average index value.

Given a regression model for domestic car sales, with known values for DCS per PR and the quarter being the first, calculate the predicted DCS using the model. Options provide different numerical predictions.

Identify which statistic indicates a perfect model fit. Choices include R²=1 or 100%, R²=0, Durbin-Watson=2, t-test for slope > 2, or None of the above.

Interpret what the "third quick check" reveals in the context of the domestic car sales regression model. Options relate to the adjusted R-square, serial correlation, seasonality, and trend in the data.

Paper For Above instruction

The evaluation of regression models in statistical analysis hinges upon several diagnostic tests that assess different aspects of model performance and validity. Among these, the Coefficient of Determination, denoted as R², stands out as the primary measure used by researchers to claim that their model explains a certain percentage of the variation in the dependent variable. This metric quantifies how well the independent variables account for the variability in the dependent variable, providing a straightforward interpretation of the model’s explanatory power. An R² close to 1 indicates that a substantial portion of the variability is explained by the model, thus allowing researchers to assert the model's effectiveness in capturing underlying dynamics (Draper & Smith, 1998). Conversely, the Durbin-Watson test evaluates the presence of autocorrelation in residuals, which is critical for time-series data, but it does not directly measure the proportion of variance explained, and hence, it cannot be used to claim explanatory power.

Turning to the analysis of seasonal indices, these are utilized to measure the seasonal effect on sales over different quarters within a fiscal year. A typical seasonal index aims to normalize seasonal fluctuations, and it is generally expected that the sum of seasonal indices over a complete cycle (four quarters in this case) should be equal to the number of quarters, which is 4, ensuring the average seasonality is centered approximately around 1 (Hyndman & Athanasopoulos, 2018). A seasonal index of 0.75 indicates that sales during that quarter are 25% below the average, while an index of 1.1 suggests a 10% above-average performance. The range of these indices is not strictly limited between zero and 2; instead, indices can theoretically be any positive number, but practical indices are usually within this range for reasonable seasonality. The statement claiming the index must be between zero and 2 is not correct, as indices can sometimes fall outside this range depending on the data.

For the regression of domestic car sales, calculating the predicted sales involves substituting the known values into the regression equation. Suppose the regression model is specified such that DCS can be predicted based on PR (percent of some measure, perhaps price or promotion), with given constants allowing computation. Using the provided variables (DCS = $10,000 per PR=10%), and assuming the model’s intercept and slope are known, the predicted DCS can be calculated as follows: DCS = intercept + slope * PR. The options given, such as $6,545,858, or $466,054.96, represent potential outputs based on such calculations. Typically, the process involves straightforward substitution, but the exact prediction depends on the model coefficients (Gujarati & Porter, 2009).

The notion of a perfect model fit is often associated with the R-squared value, which indicates the proportion of variance explained by the model. An R² of 1, or 100%, signifies a perfect fit where the model accounts for all variability in the dependent variable; thus, the statement "R²= 1 or 100%" correctly indicates a perfect fit (Kutner et al., 2005). Other options, like R²=0, or Durbin-Watson=2, pertain to different aspects of the model's diagnostics, but do not directly signal a perfect fit. The Durbin-Watson statistic, for example, assesses autocorrelation in residuals, with a value close to 2 indicating no autocorrelation, but it does not measure the explained variance.

The "third quick check" in regression analysis typically refers to assessing the robustness or the explanatory power of the model, often via the adjusted R-square, which adjusts for the number of predictors and sample size. A high adjusted R-square suggests that a large portion of the variability in the dependent variable is explained, taking model complexity into account (Kuhn & Johnson, 2013). This check can also involve residual analysis to examine serial correlation or seasonality. In the context provided, most likely, it indicates that more than three-quarters of the variation is explained, reinforcing the model's strong explanatory power.

References

• Draper, N. R., & Smith, H. (1998). Applied Regression Analysis (3rd ed.). Wiley-Interscience.
• Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill Education.
• Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice. OTexts.
• Kuhn, M., & Johnson, K. (2013). Applied Predictive Modeling. Springer.
• Kutner, M. H., Nachtsheim, C., Neter, J., & Li, W. (2005). Applied Linear Regression. McGraw-Hill Education.