https://file.aiquickdraw.com/mathbot/file/1726696102894d9kmb0r4.jpg

Let's break down the tasks from the image:

### Task 2: A company wants to understand the relationship between their online ad spend and sales revenue.

The provided data is as follows:

| Ad Spend (P) | Sales Revenue (P) |
|--------------|-------------------|
| 500          | 7,000             |
| 1,000        | 12,000            |
| 1,500        | 15,000            |
| 2,000        | 18,000            |
| 2,500        | 22,000            |

**a. Fit a linear regression model for the data provided.**

We can calculate the linear regression equation, \( y = mx + b \), where:
- \( y \) is the sales revenue,
- \( x \) is the ad spend,
- \( m \) is the slope, and
- \( b \) is the y-intercept.

Let me calculate that for you.The linear regression equation based on the given data is:

\[
y = 7.2x + 4000
\]

where:
- \( y \) is the sales revenue,
- \( x \) is the ad spend,
- 7.2 is the slope, and
- 4000 is the y-intercept.

### Next Steps:
- **b. Use the regression equation to predict sales revenue for an ad spend of P3,000.**
Let me calculate that next.For an ad spend of P3,000, the predicted sales revenue is **P25,600** using the linear regression model.

### Now, let's move to the next part:
- **c. Calculate the correlation coefficient** between ad spend and sales revenue.The correlation coefficient between ad spend and sales revenue is approximately **0.9954**. This indicates a very strong positive linear relationship between the two variables.

### Finally:
- **d. Interpret the correlation coefficient and discuss its significance in digital marketing strategies.**

The correlation coefficient of **0.9954** suggests that there is a very strong linear relationship between the amount spent on ads and the sales revenue. This implies that increases in ad spending are highly correlated with increases in sales revenue. In digital marketing strategies, such a strong relationship highlights the importance of investing in advertisements, as higher spending can directly lead to significant boosts in sales.

Would you like further details or have any questions?

### Here are 5 related questions for further exploration:
1. How would changes in the dataset (e.g., outliers) affect the regression model?
2. Can we generalize this linear model for higher ad spend amounts?
3. What factors could cause deviations from this linear trend in real-world scenarios?
4. How can we assess whether this model is overfitting or underfitting?
5. How can the R-squared value provide additional insights into model performance?

**Tip:** Always plot your data along with the regression line to visually assess the fit and detect any potential anomalies.

A company wants to understand the relationship between their online ad spend and sales revenue. The following data is collected: Ad Spend (P) and Sales Revenue (P) with the given values. Tasks include fitting a linear regression model, predicting sales revenue for P3000 ad spend, calculating the correlation coefficient, and interpreting the correlation coefficient in digital marketing.

Learn how to fit a linear regression model to analyze the relationship between online ad spend and sales revenue. This problem involves predicting sales revenue for an ad spend of P3000, calculating the correlation coefficient, and interpreting its significance in digital marketing strategies. Suitable for undergraduate students.

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