https://file.aiquickdraw.com/mathbot/file/1726663191233aegrv4zt.jpg

Let's go through the questions and their answers based on the image:

### Question 92:
**Which one of the following statements is correct regarding the limit of the two regression coefficients?**
- (A) No limit
- (B) Must be positive
- (C) One positive and the other negative
- (D) **Product of the regression coefficients must be numerically less than unity.**

The marked correct answer is **(D)**, which is correct. The product of the regression coefficients is always numerically less than 1.

---

### Question 93:
**In case of "Insurance companies' profits" and "The number of claims they have to pay," there exists a:**
- (A) Positive correlation
- (B) **Negative correlation**
- (C) No correlation
- (D) It cannot be predicted

The marked correct answer is **(B)**, which is correct. There is a negative correlation between insurance companies' profits and the number of claims.

---

### Question 94:
**The variance of two variables `x` and `y` are 16 and 25 and covariance between `x` and `y` is 18.5. Another two variables `u` and `v` are defined as `u = (x - 3)/2` and `v = (y - 2)/3`, then the coefficient of correlation between `u` and `v` is:**
- (A) 0.85
- (B) 0.875
- (C) 0.90
- (D) 0.925

The answer marked is **(D)**, but let's verify the calculation:
Given:
- Variance of `x` = 16, so \( \sigma_x = 4 \)
- Variance of `y` = 25, so \( \sigma_y = 5 \)
- Covariance between `x` and `y` = 18.5
The formula for the correlation coefficient is:
\[
r_{xy} = \frac{\text{Cov}(x,y)}{\sigma_x \sigma_y} = \frac{18.5}{4 \times 5} = 0.925
\]

Thus, the correct answer is indeed **(D) 0.925**.

---

### Question 95:
**Which of the following statements is correct?**
- (A) Both regression coefficients must be less than unity.
- (B) Regression coefficients are independent of origin and scale.
- (C) The regression lines of two independent variables are parallel to each other.
- (D) **If two regression lines coincide with each other, there is no correlation between the variates.**

The marked correct answer is **(D)**, which is correct. If the two regression lines coincide, there is no variation, thus no correlation.

---

Would you like further details on any of these answers, or do you have any questions?

### Follow-up Questions:
1. How is the product of regression coefficients related to the correlation coefficient?
2. What happens if both regression coefficients are positive?
3. Why is there a negative correlation between insurance company profits and claims?
4. How do you calculate the correlation coefficient from variances and covariance?
5. What would the regression coefficients be if the correlation is perfect?

### Tip:
When solving problems involving regression or correlation, understanding the underlying relationships between variables is key to interpreting the coefficients correctly.

Which one of the following statements is correct regarding the limit of the two regression coefficients?

Explore how to determine the limits of regression coefficients and their relationship with correlation, including key formulas and concepts used in undergraduate statistics.

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