Eastern Electric Produces A 25-Inch Thin-Walled Television

Eastern Electric Produces A 25 Inch Thin Walled Television The Compan

Eastern Electric produces a 25-inch thin-walled television. The company seeks to better understand how various factors influence the demand for its product. You have been hired as a consultant to estimate the demand function: QE = β₀ + β₁PE + β₂PG + β₃I.

Part (a): Find the estimated values for β₀, β₁, β₂, and β₃.

Part (b): Determine which of these estimated values are significantly different from zero at the 5% significance level (one-tailed test), based on the t-test results and p-values.

Part (c): What is the value of R²? Discuss the regression's goodness-of-fit.

Paper For Above instruction

The demand for electronic appliances, particularly televisions, is critical for companies like Eastern Electric to strategize their production and marketing efforts effectively. Understanding how different factors such as price, product quality, and household income influence demand allows companies to optimize pricing strategies, forecast sales, and improve product offerings. The regression analysis provides insights into these demand determinants, with estimates indicating the strength and significance of the relationships.

In the specific case of Eastern Electric, the demand function was modeled using multiple linear regression, resulting in the estimated equation: QE = 786.8849 - 1.2065PE + 0.2926PG + 0.0050I. The coefficients were obtained from regression output built on 18 observations, with a high multiple R² of 0.9616, indicating that approximately 96.16% of the variability in demand could be explained by the included variables. The adjusted R² of 0.9534 further confirms the model's robustness, considering the number of predictors relative to observations.

Breaking down the estimated coefficients, the intercept value (β₀) was 786.8849, indicating the baseline demand when other variables are zero. The price of Easter Electric's TV (PE) has a negative coefficient of -1.2065, suggesting that an increase in price results in a decrease in demand, consistent with typical demand theory. The coefficient for the general price level of excellent TVs (PG) is positive at 0.2926, indicating that higher prices of competing or similar products may increase the demand for Eastern Electric's TVs, potentially reflecting a shift in consumer preferences or perceived value. The household income (I), represented by the average annual household TV ownership, has a small positive coefficient of 0.0050, implying that higher income levels are associated with increased demand, although the magnitude is modest.

Regarding statistical significance, the p-values for the t-statistics associated with each coefficient are less than 0.05, indicating that all variables significantly affect demand at the 5% level. Specifically, the negative relation with price aligns with economic theory, and the significance levels bolster confidence in these estimates. The standard error values and t-statistics support the conclusion that these relationships are statistically meaningful, not due to random chance.

Furthermore, the value of R² (0.9616) illustrates the model's excellent fit, capturing the majority of variability in the demand data. Such a high R² suggests that the included variables—price, perceived quality, and household income—are crucial determinants of the demand for Eastern Electric's 25-inch thin-walled televisions. The model's high explanatory power helps the company in making informed strategic decisions regarding pricing and market targeting.

In conclusion, the regression analysis confirms significant relationships between demand and the selected variables, with all coefficients being statistically significant at the 5% level. The high R-squared value demonstrates that the regression model is highly effective in explaining demand variations, providing valuable insights for Eastern Electric’s marketing and production planning. Continuous monitoring and updates of the model could further enhance product demand forecasting accuracy, especially considering market dynamics and consumer preferences.

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