The marketing division of an electronics company is analyzing the relationship between the amount they spent advertising a product and the number of units of the product sold. They analyzed monthly data from the past six months. The data they analyzed are shown below.
 
Advertising Expense
(thousands of dollars)	Units of Product Sold
5.2 	20,000
6.1	22,500
6.4	23,200
7.1 	25,600
9.4 	28,100
10.2	29,000

Select all the statements that correctly interpret the value of the correlation coefficient for these data.
A. As the amount spent on advertising a product increases, the number of units of the product sold also increases.
B.There is a positive association between the amount spent on advertising and the number of units of the product sold.
C.There is a negative association between the amount spent on advertising and the number of units of the product sold.
D.A linear model can be used to represent the relationship between the amount spent on advertising and the number of units of the product sold.
E.The slope of a line that models the relationship between the amount spent on advertising and the number of units of the product sold is 0.97.

Let's analyze the given statements based on the correlation between advertising expense and product units sold.

### 1. **As the amount spent on advertising a product increases, the number of units of the product sold also increases.**  
- **Correct (A):** Since the data shows that with increased advertising expenses, the number of units sold consistently increases, this suggests a positive relationship between the two variables.

### 2. **There is a positive association between the amount spent on advertising and the number of units of the product sold.**  
- **Correct (B):** This is another way of saying that as advertising expenses increase, sales increase, indicating a positive correlation.

### 3. **There is a negative association between the amount spent on advertising and the number of units of the product sold.**  
- **Incorrect (C):** The relationship is positive, not negative. A negative association would mean that increasing advertising would lead to a decrease in sales, which is not the case here.

### 4. **A linear model can be used to represent the relationship between the amount spent on advertising and the number of units of the product sold.**  
- **Correct (D):** Based on the data, a linear model seems reasonable because the relationship between advertising expense and units sold appears to increase steadily.

### 5. **The slope of a line that models the relationship between the amount spent on advertising and the number of units of the product sold is 0.97.**  
- **Not necessarily (E):** The slope mentioned in this statement is not provided or calculated explicitly in the data given. The actual slope must be calculated using regression methods, and there's no indication from the provided data that the slope is 0.97.

### Correct Responses:
- **A, B, and D**

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Would you like me to calculate the correlation coefficient or explain how to determine the slope of a regression line?

Here are five related questions:
1. How can the correlation coefficient be calculated from given data points?
2. What does a correlation coefficient close to 1 imply?
3. How is a regression line for linear models calculated?
4. What other factors might influence the number of units sold besides advertising expenses?
5. Can a nonlinear model be better in some cases even if a linear model seems reasonable?

**Tip:** The correlation coefficient measures the strength and direction of a linear relationship.

The marketing division of an electronics company is analyzing the relationship between the amount they spent advertising a product and the number of units of the product sold. They analyzed monthly data from the past six months. The data they analyzed are shown below.

Advertising Expense (thousands of dollars)	Units of Product Sold
5.2	20,000
6.1	22,500
6.4	23,200
7.1	25,600
9.4	28,100
10.2	29,000

Select all the statements that correctly interpret the value of the correlation coefficient for these data.

Explore the relationship between advertising expenses and units sold with data analysis from an electronics company. Learn how to interpret correlation, calculate linear models, and understand the positive association in this problem. Suitable for high school students in Grades 10-12.

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