Question 1: ABC Corporation Has Used Regression Analysis To

Question 1abc Corporation Has Used Regression Analysis To Perform Pr

Question 1: ABC Corporation has used regression analysis to perform price elasticity analysis. In doing so management regressed the quantity demanded (y variable) against price (x variable) with the following results: Multiple R .86798 Adjusted R squared .72458, Standard error 542.33 Intercept 56400.50 Price coefficient –4598.20 What percentage of the variation in quantity demanded is explained by price? A) 86.798% B) 72.45% C) 56.4% D) 54.23%

Paper For Above instruction

Regression analysis is a fundamental statistical technique employed to understand the relationship between a dependent variable and one or more independent variables. In the context of ABC Corporation's price elasticity analysis, the regression examines how changes in price influence the quantity demanded of a product. The provided regression output details several key statistics that allow us to interpret the model's explanatory power and the nature of the relationship between price and demand.

The coefficient of determination, denoted as R squared (or R²), measures the proportion of total variability in the dependent variable that is explained by the independent variables included in the model. An R squared value ranges from 0 to 1, where a higher value indicates a better fit of the model to the observed data. In this scenario, the multiple R is given as 0.86798, which is the correlation coefficient between observed and predicted values of demand. The R squared is the square of this correlation coefficient: R² = (0.86798)² ≈ 0.7537, or about 75.37%. This percentage indicates that approximately 75.37% of the variation in the quantity demanded is explained by the price variable in this regression model.

However, the regression output also provides the adjusted R squared of 0.72458, or roughly 72.46%. Adjusted R squared accounts for the number of predictors in the model relative to the sample size, penalizing excess variables that do not improve the model considerably. It offers a more conservative but reliable estimate of the model's explanatory power, especially when multiple predictors are involved. Since only one predictor (price) appears to be in the model, the adjusted R squared closely aligns with R squared, indicating the model's goodness-of-fit is stable and meaningful. Therefore, based on the information provided, about 72.46% of the variation in demand is explained by price, according to the adjusted R squared.

Given the multiple-choice options, the closest match to the adjusted R squared value of approximately 72.46% is option B) 72.45%. Therefore, the correct answer to the first question is B) 72.45%.

In conclusion, the R squared value—specifically the adjusted R squared—is used to interpret how well the price variable explains the variation in demand within this regression model. The high R squared underscores a strong relationship, suggesting that price has a significant impact on demand, consistent with economic theory regarding price elasticity. This measure guides managers and analysts in understanding how sensitive customer demand is to price changes, informing pricing strategies and revenue optimization efforts.

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