The image shows a worksheet involving data analysis on the effectiveness of advertising campaigns. It has a table of data with two columns: "Advertising" (in dollars) and "Items sold." The tasks require:

1. Graphing the data with appropriate scales and axes (Advertising on the x-axis and Items Sold on the y-axis).
2. Calculating averages of advertising amounts and items sold.
3. Adding averages as a point to the scatterplot.
4. Giving the equation of the Line of Best Fit (regression line).
5. Drawing the line on the scatterplot.
6. Interpreting the slope and y-intercept in context.
7. Evaluating the scatterplot using Pearson’s correlation coefficient.
8. Concluding if advertising helps increase sales based on the correlation.

Let's go through each step:

Step (a): Graphing the Data You will need to plot advertising dollars on the x-axis and items sold on the y-axis. Each point on the graph represents a month's data from the table provided.

Step (b): Calculating Averages

• The average for advertising is: $\text{Average} = \frac{45 + 55 + 75 + 47 + 91 + 100 + 120 + 75 + 90 + 85 + 58}{11} = \frac{841}{11} \approx 76.45$
• The average for items sold is: $\text{Average} = \frac{15 + 25 + 37 + 13 + 29 + 47 + 61 + 41 + 50 + 45 + 30}{11} = \frac{393}{11} \approx 35.73$ You can add this point (76.45, 35.73) to your scatterplot.

Step (c): Line of Best Fit To find the line of best fit, you would typically use linear regression. If you plot the points, the equation will likely follow the form: $y = mx + b$ Where $m$ is the slope and $b$ is the y-intercept.

Step (f) & (g): Interpretation of Slope and Y-intercept

• Slope represents the rate at which items sold increases per additional dollar spent on advertising.
• Y-intercept indicates the expected number of items sold when no money is spent on advertising.

Step (h): Pearson Correlation Coefficient This statistic measures the strength of the relationship between advertising and items sold. A strong positive $r$ indicates that higher advertising spending correlates with higher sales.

Step (j): Conclusion If $r$ is strongly positive, we can suggest that increased advertising leads to increased sales. However, correlation does not imply causation, and other factors may be influencing sales as well.

Would you like help calculating the equation for the line of best fit or further details on any of these steps?

Here are 5 related questions:

1. How do we calculate the slope of a line from data points?
2. What does a Pearson correlation coefficient of +1 indicate about the data?
3. How can you determine if a scatterplot shows a linear relationship?
4. Why is it important to consider the y-intercept in regression analysis?
5. What other factors might affect the relationship between advertising and sales?

Tip: When interpreting a graph, always check if the scale of the axes is appropriate for visualizing the relationship accurately.