https://r2.erweima.ai/mathbot/image/17262644132883kmg0jlp.jpg

Let's break down the tasks in the image you provided:

1. **Task 1: Scatter Plot for Table 5.11**
   - The table provides the following values for $X$ and $Y$:
     - $ X = -2, Y = -3 $
     - $ X = -1, Y = -1 $
     - $ X = 0, Y = 2 $
     - $ X = 1, Y = 0 $
     - $ X = 2, Y = 3 $

   You need to create a scatter plot by plotting these points on a Cartesian plane.

2. **Task 2: Scatter Plot for Table 5.12**
   - The second table provides different values of $X$ and $Y$:
     - $ X = -2, Y = -2 $
     - $ X = -1, Y = 0 $
     - $ X = 0, Y = 2 $
     - $ X = 1, Y = 3 $
     - $ X = 2, Y = 6 $

   Similar to Task 1, plot these points on a scatter plot.

3. **Task 3: Correlation Between Advertising Spending and Sales**
   - The table shows:
     - For $ \$143.8 $ spent on advertising, 855 units were sold.
     - For $ \$91.7 $, 360 units were sold.
     - For $ \$43.8 $, 170 units were sold.
     - For $ \$26.7 $, 130 units were sold.
   
   This asks whether there is a relationship between advertising spending and sales. To answer this, you would typically compute the correlation coefficient (Pearson's $ r $).

4. **Task 4: Expected Correlation**
   - Without seeing the data, you are asked to predict the type of correlation you would expect in various scenarios (positive, negative, or none).
     - a) Age of people and running speed.
     - b) Number of store clerks and volume of sales.
     - c) Age of people and life satisfaction.
     - d) A man’s height and number of hairs on his head.

Let me first solve Task 3 (correlation coefficient) using the given data for advertising expenses and sales. I'll calculate the correlation coefficient and provide you with the result.The correlation coefficient between advertising spending and sales is approximately **0.97**. This indicates a very strong positive correlation, meaning that as advertising spending increases, sales tend to increase significantly as well.

Would you like further details or have any questions about these results?

Here are 5 related questions that could deepen your understanding:

1. How is the Pearson correlation coefficient calculated?
2. How can you interpret different ranges of correlation coefficients (e.g., weak, moderate, strong)?
3. What would the scatter plot of the advertising data look like?
4. How could outliers affect the correlation coefficient?
5. Can correlation imply causation in this case, or are there other factors to consider?

**Tip**: Correlation measures the strength and direction of a linear relationship, but it doesn't imply that one variable directly causes changes in the other.

Based on the tables provided, create scatter plots for the given data and analyze the correlation between advertising spending and sales.

Learn how to create scatter plots for two datasets and analyze the correlation between advertising spending and sales. This problem covers key statistical concepts, including data interpretation and Pearson's correlation coefficient, suitable for Grades 9-12.

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