Here Are The Basics Of The Assignment Question 10 50a Golf C

Here are The Basic Of the Assignmentquestion 10 50a Golf Club Manufac

Here are the basic of the assignment: Question 10-50 A golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales. a) Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = ab^X), and multiplicative (Y = aX^b). Which equation fits the data best? b) Interpret your best-fitting equation. c) Using the best-fitting equation, predict sales during a month in which the price is $470. Question 12-64 Let Y_t be the sales during month t (in thousands of dollars) for a photography studio, and let P_t be the price charged for portraits during month t. The data are in the file P11_45.xlsx. Use regression to fit the following model to these data: Y_t = a + b₁Y_t-1 + b₂P_t + e_t This equation indicates that last month’s sales and the current month’s price are explanatory variables. The last term, e_t, is an error term. a. If the price of a portrait during month 21 is $10, what would you predict for sales in month 21? b. Does there appear to be a problem with autocorrelation of the residuals?

Paper For Above instruction

The analysis of the relationship between price and demand, as well as the examination of sales dynamics over time, provides valuable insights into consumer behavior and market trends. This paper interprets two interconnected datasets involving a golf club manufacturer and a photography studio, employing regression techniques to understand pricing effects and temporal dependencies.

Part 1: Demand Analysis for Golf Clubs

The first dataset (P10_50.xlsx) explores how the price of golf clubs influences monthly sales. To model this relationship, three functional forms are fitted: linear, exponential, and multiplicative. The linear model assumes a direct, proportional change in demand with respect to price, represented as Y = a + bX, where Y is sales and X is price. The exponential model, Y = ab^X, captures multiplicative effects where sales change exponentially with price, while the multiplicative model, Y = aX^b, indicates power-law relationships.

Regression analysis reveals that among these models, the exponential model often provides the best fit for demand data because it captures the diminishing effect of rising prices more accurately in many real-world market scenarios. Empirical fitting involves estimating parameters a and b using least squares or non-linear regression techniques. The goodness-of-fit measures, such as R-squared and residual analysis, determine the most suitable model.

Upon identifying the best-fitting model—suppose the exponential model—we interpret its parameters: the constant 'a' reflects baseline sales when price approaches zero, and 'b' indicates the rate at which sales change with price. A negative 'b' would suggest that increasing the price reduces demand exponentially, aligning with economic theory.

Using this model, a prediction for sales at a specified price point can be generated. For instance, when the price is $470, the model’s parameters are employed to estimate expected sales, aiding in pricing strategies and inventory planning.

Part 2: Sales Dynamics of a Photography Studio

The second dataset (P11_45.xlsx) examines the influence of previous month’s sales and current month’s portrait prices on current sales. Here, a multiple regression model is specified: Y_t = a + b₁Y_t-1 + b₂P_t + e_t. The inclusion of lagged sales accounts for autocorrelation or inertia in sales figures, while the current price reflects pricing decisions.

To predict sales for month 21 given the portrait price of $10, the estimated regression coefficients must be applied to the known values. If prior sales and the estimated parameters are known, one can calculate the expected sales, thus facilitating revenue forecasting and marketing decisions.

Furthermore, analyzing residuals from the regression assesses autocorrelation, which can inflate Type I error rates and distort inference. The Durbin-Watson statistic or plots of residuals can indicate whether residuals are correlated across time, suggesting the need for model adjustments such as including additional lags or transforming variables.

Conclusion

This study highlights the importance of selecting suitable functional forms in demand modeling, distinguishing between linear, exponential, and power-law relationships. Accurate model fitting enhances predictive capabilities, informing strategic decisions in pricing and sales forecasting. Additionally, accounting for autocorrelation in time series models is crucial for valid inference, emphasizing the importance of diagnostic testing in regression analysis. Overall, integrating demand estimation with temporal dynamics provides a comprehensive understanding of sales behavior in market settings.

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