Activity1

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Economics

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Feb 20, 2024

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Activity I - A manager claims that increases in advertising expenditure will surely raise the firm's profits, citing his sense that people find the firm's ads entertaining. 1. Sketch how you might refute this claim using: a. A theoretical argument Theoretical Argument: 1. Diminishing Returns: Theoretically that there is a point of diminishing returns when it comes to advertising expenditure. Initially, increasing advertising may lead to higher brand awareness and sales, but beyond a certain threshold, additional spending may not yield significant additional profits. This can be explained using economic theory, such as the law of diminishing marginal returns. 2. Market Saturation: In some markets, it's possible that you've already reached a point where most potential customers are aware of your product or service. Further advertising may not significantly expand your customer base or increase sales. 3. Quality vs. Quantity: Emphasize that the quality of advertising content matters as much as, if not more than, the quantity of advertising expenditure. Even if ads are entertaining, if they don't effectively communicate the product's value or relevance, they may not drive sales. Data Analysis: 1. Historical Data: Analyze historical sales data in relation to advertising expenditure. You can create a scatter plot or time series analysis to see if there's a point at which increasing advertising spending no longer correlates with a proportional increase in profits. 2. A/B Testing: Conduct A/B tests where you allocate different levels of advertising spending to different groups or regions. Compare the sales and profit performance between these groups. If you find that increased spending doesn't consistently lead to higher profits, it will challenge the claim. 3. Competitor Analysis: Examine the advertising strategies of competitors in your industry. If they are not significantly outspending you but are achieving comparable or better results, it suggests that there are other factors at play beyond just ad spend. Refutation using data is often more convincing for several reasons: 1. Empirical Evidence: Data provides empirical evidence based on actual observations and outcomes. It reflects real-world scenarios and behaviors, making it more tangible and credible than theoretical arguments, which are based on abstract concepts and assumptions.

2. Objectivity: Data analysis is typically perceived as more objective because it relies on concrete numbers and measurements. It reduces the influence of personal biases and subjective opinions, making the argument more robust. 3. Quantitative Analysis: Data allows for quantitative analysis, which means you can measure the impact of variables and relationships precisely. This quantification provides clarity and precision in your argument, making it easier for others to understand and accept. 4. Visualization: Data can be visualized effectively through charts, graphs, and statistical summaries. Visual representations of data make it easier for people to grasp complex relationships and trends quickly. A well-constructed graph can illustrate the point more effectively than a lengthy written explanation. 5. Comparisons and Trends: Data analysis often involves comparing different scenarios, groups, or time periods. These comparisons can reveal whether a particular claim holds consistently across various situations or if it's an isolated case. In summary, refuting claims using data is more convincing because it relies on real-world evidence, objectivity, quantification, visualization, and the ability to inform decision-making. Data-driven arguments are generally more compelling and persuasive because they are grounded in facts and observations rather than theoretical speculation. Activity II - A grocery store manager is interested in the data-generating process for her store's weekly soda sales. She believes factors impacting these sales include price, product placement, and whether the week contains a holiday. Write out a formal representation of the data- generation process for weekly soda sales that incorporates these and additional factors. Let's create a formal representation of the data-generation process for weekly soda sales, considering factors like price, product placement, and the presence of holidays. This can be expressed as a linear regression model: Soda Sales (Y) = β0 + β1 * Price + β2 * Product Placement + β3 * Holiday + ε Where:  Y is the weekly soda sales (the dependent variable).  Price is the price of soda products during the week.  Product Placement is a binary variable (1 for prime product placement, 0 for regular).  Holiday is a binary variable (1 if the week contains a holiday, 0 otherwise).  β0 is the intercept, representing the baseline weekly sales when all other factors are zero.

 β1 , β2 , and β3 are the coefficients representing the effect of each respective factor on weekly soda sales.  ε represents the error term, accounting for random variations and unexplained factors. This linear regression model assumes that the weekly soda sales are influenced by these factors linearly. The coefficients ( β1 , β2 , and β3 ) represent how much the sales are expected to increase or decrease for a one-unit change in each respective factor, holding other factors constant. To use this model effectively, we would need to estimate the coefficients using historical sales data and statistical techniques like ordinary least squares regression. Once estimated, we can make predictions about future weekly soda sales based on the values of these factors, helping the grocery store manager make informed decisions regarding pricing, product placement, and holiday promotions. Activity III - Access the dataset Sales and Costs.xlsx (See the attached) and answer the following questions. To calculate the requested descriptive statistics, we'll perform the following calculations step by step: 1. Calculate the Mean (Average) of Sales: To find the mean of sales, you need to sum up all the sales values and divide by the total number of regions (in this case, 241 regions). Mean of Sales = (Sum of Sales) / (Total Number of Regions) Sum of Sales = Σ(Sales) for all regions Sum of Sales = $ 357,500,286 (the sum of all sales values) Total Number of Regions = 241 Mean of Sales = $ 357,500,286 / 241 ≈ $ 1,483,403.676 2. Calculate the Variance of Materials Costs: To find the variance of materials costs, we'll use the following formula: Variance = Σ((X - X̄)²) / (N - 1) Where: o X is each materials cost value. o X̄ (X-bar) is the mean of materials costs. o N is the total number of regions (240 in this case).

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First, calculate the mean of materials costs (X̄): X̄ = (Sum of Materials Costs) / (Total Number of Regions) Sum of Materials Costs = Σ(Materials Costs) for all regions Sum of Materials Costs = $5,707,400 (the sum of all materials costs values) X̄ = $5,707,400 / 241 ≈ $23682 Now, calculate the variance: Variance = Σ((Materials Costs - X̄)²) / (240 - 1) Variance = Σ((Materials Costs - $23682)²) / (240 - 1) Variance of Materials Costs ≈ [($2,759,592,352)) / 240] Variance of Materials Costs ≈ $11,498,301.47 3. Calculate the Covariance of Labor Costs and Materials Costs: The covariance between two variables, in this case, labor costs and materials costs, can be calculated using the following formula: Covariance = [(Σ(Labor Costs - Mean of Labor Costs) * (Materials Costs - Mean of Materials Costs)) / (Number of Regions - 1)] First, we need to calculate the Mean of Labor Costs: Sum of Labor Costs = $59,313.00 + $84,294.00 + ... + $58,677.00 Sum of Labor Costs = $17,450,911.00 Mean of Labor Costs = $17,450,911/ 241 Mean of Labor Costs ≈ $72,410 Now, calculate the covariance: Covariance ≈ [(Σ($59,313.00 - $72,410) * ($25,489.00 - $23,682) + ... + ($58,677.00 - $72,410) * ($28,344.00 - $23,682)) / 240] Covariance ≈ [(Σ ($762946962)) / 240] Covariance ≈ $ 31,78,945.675 (approximately) 4. Mean of Labor Costs (already calculated above):

Mean of Labor Costs ≈ $72,410. 5. Total Sales: Total Sales = Sum of Sales Total Sales = $357,500,286 Calculate at least two more descriptive statistics for this dataset. 6. Range of the Materials Costs To find the range, follow these steps:  Order all values in your data set from low to high.  Subtract the lowest value from the highest value.  R = range  H = highest value  L = lowest value R=H-L Range of Materials Costs= $29,471 - $17,557 = $ 11,914 7. Standard deviation of the Material costs To find the standard deviation, we take the square root of the variance (calculated in section 2) Standard Deviation= √ Variance = 3390.91

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