Is there a relation between the age difference between​ husband/wives and the percent of a country that is​ literate? Researchers found the​ least-squares regression between age difference​ (husband age minus wife​ age), y, and literacy rate​ (percent of the population that is​ literate), x, is ModifyingAbove y with caretyequals=negative 0.0495−0.0495xplus+6.66.6. The model applied for 2424less than or equals≤xless than or equals≤100100. Complete parts​ (a) through​ (e) below.
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Part 1
​(a) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice.
For every unit increase in 
▼ 
age difference,
literacy rate,
 the 
▼ 
age difference
literacy rate
 falls by enter your response here ​units, on average.
​(Type an integer or decimal. Do not​ round.)

The regression equation given is:

\[
y = -0.0495x + 6.6
\]

where \( y \) represents the **age difference** (husband's age minus wife's age) and \( x \) represents the **literacy rate** (percent of the population that is literate).

### Interpretation of the slope:
The slope of the regression line is \(-0.0495\). This indicates that for every unit increase in **literacy rate**, the **age difference** falls by 0.0495 units, on average.

Thus, the correct interpretation is:

For every unit increase in **literacy rate**, the **age difference** falls by 0.0495 units, on average.

### Summary:
- **Slope**: \(-0.0495\) implies a negative relationship between literacy rate and age difference. 
- **Interpretation**: As literacy rate increases, the age difference decreases.

Would you like further details or clarification? Here are some related questions for deeper understanding:

1. What does the intercept \(6.6\) represent in this context?
2. How would you interpret the prediction for a country with 80% literacy rate?
3. What is the significance of the range \(24 \leq x \leq 100\) in this model?
4. How can the residuals help assess the fit of this model?
5. What assumptions must be met for this linear regression to be valid?

**Tip**: Always check if the slope sign matches the expected direction of the relationship in real-world context!

Is there a relation between the age difference between​ husband/wives and the percent of a country that is​ literate? Researchers found the​ least-squares regression between age difference​ (husband age minus wife​ age), y, and literacy rate​ (percent of the population that is​ literate), x, is y = -0.0495x + 6.6. The model applied for 24 ≤ x ≤ 100. Complete parts​ (a) through​ (e) below.

Explore the relationship between age difference and literacy rate through linear regression. This analysis covers the least-squares regression model, interpreting the slope and intercept, and understanding the negative correlation between literacy rate and age difference. Suitable for students in Grades 10-12.

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