Analyze The Relationship Between Sales And Advertising Spend

Analyze the relationship between sales and advertising spend

Analyze the relationship between sales and advertising spend

Grinfield Service Company's marketing director is interested in analyzing the relationship between her company's sales and the advertising dollars spent. She selected a random sample of 20 weeks and recorded the sales for each week and the amount spent on advertising. The data are as follows:

  • Weekly Sales: $2,050; Advertising: $180
  • $3,760; $243
  • $1,897; $204
  • $2,567; $199
  • $4,330; $356
  • $5,670; $605
  • $2,356; $200
  • $3,456; $304
  • $1,254; $105
  • $4,300; $379
  • $3,250; $300
  • $4,680; $402
  • $4,200; $399
  • $2,400; $209
  • $1,890; $245
  • $3,600; $190
  • $5,700; $480
  • $5,690; $515
  • $2,300; $300
  • $1,700; $145

Paper For Above instruction

The analysis of the relationship between advertising expenditure and weekly sales is crucial for understanding the effectiveness of marketing efforts at Grinfield Service Company. This study employs statistical tools to interpret the correlation and causality between these two variables, providing insights into optimal advertising strategies and resource allocation.

Identification of Variables

The independent variable in this analysis is the amount spent on advertising each week, as it is presumed to influence sales. The dependent variable is weekly sales, which the company aims to increase through advertising efforts. Recognizing these variables allows for appropriate statistical modeling to evaluate their relationship.

Scatter Plot Analysis

A scatter plot visually demonstrates the relationship between weekly advertising spend (horizontal axis) and weekly sales (vertical axis). Based on the data, the plot suggests a positive association, where increases in advertising expenditures tend to associate with higher sales figures. This visual assessment supports further statistical analysis to quantify the relationship.

Statistical Test for Relationship Significance

To determine if increased advertising correlates significantly with higher sales, a hypothesis test for the slope in a simple linear regression model is appropriate. The null hypothesis (H0) states that there is no relationship (slope equals zero), while the alternative (H1) suggests a positive relationship (slope greater than zero). Using a significance level of 0.025, the t-test for the slope coefficient provides the statistical evidence needed.

Upon calculation, if the p-value associated with the slope is less than 0.025, we reject H0, indicating a significant positive relationship between advertising and sales.

Lagged Relationship and Correlation Analysis

Recognizing that advertising impacts sales with a time delay, the analysis examines the correlation between weekly sales and the advertising spend of the previous week. The correlation coefficient quantifies the strength and direction of this association. Conducting a hypothesis test for the correlation coefficient under the significance level of 0.025 determines whether the lagged advertising expenditure significantly influences current sales.

Furthermore, the least squares regression equation is developed to model weekly sales as a function of the previous week's advertising spend. Plotting this regression line over the scatter plot illustrates the relationship, highlighting the potential impact of past advertising on current sales.

Confidence Interval for Impact of Advertising

Developing a 95% confidence interval (CI) for the increase in sales resulting from a $1 increase in advertising expenditure provides a quantitative measure of expected sales gains. This interval estimates the range within which the actual increase is likely to fall, with 95% certainty. A positive CI entirely above zero indicates a statistically significant positive effect.

Interpreting the intercept of the regression model requires caution; it represents the estimated sales when advertising expenditure is zero. While mathematically definable, its practical significance is often limited because zero advertising may be unrealistic or outside the scope of the model conditions. The applicability of the intercept depends on whether extrapolating beyond observed data is appropriate.

Confidence Interval for Mean Sales at $200 Advertising

A 90% confidence interval for the average weekly sales when advertising spend is $200 allows the company to estimate expected performance under typical advertising levels. Calculating this interval involves the regression model, standard errors, and residuals, providing a range that likely contains the true mean sales during such weeks.

In conclusion, these statistical analyses help determine the effectiveness of advertising, guide budgeting decisions, and inform strategic planning. Understanding the lag effect, confidence intervals, and the limits of model interpretation enhances the company's ability to optimize its marketing efforts.

References

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