This question requires identifying the true statements concerning lines of regression and the correlation coefficient ($r$). Key properties include:

• The product of the regression coefficients ($b_{YX}$ and $b_{XY}$) must be less than or equal to 1 ($0 \le b_{YX} \times b_{XY} \le 1$).
• This product is equal to the square of the correlation coefficient ($r^2$).
• Therefore, $0 \le r^2 \le 1$.
• If $r^2 = 1$ (i.e., $r = \pm 1$), the two regression lines must be identical.

Regression Line Analysis of Options

Option 1 Analysis

Equations: $Y = 1 + 1.8X$ and $X = 1 - 0.5Y$.

• Regression coefficient of $Y$ on $X$: $b_{YX} = 1.8$.
• Regression coefficient of $X$ on $Y$: $b_{XY} = -0.5$.
• Calculate $r^2$: $r^2 = b_{YX} \times b_{XY} = 1.8 \times (-0.5) = -0.9$.

Since $r^2$ cannot be negative, Option 1 is false.

Option 2 Analysis

Equations: $Y = 1 + 1.3X$ and $X = 2 + 1.1Y$.

• Regression coefficient of $Y$ on $X$: $b_{YX} = 1.3$.
• Regression coefficient of $X$ on $Y$: $b_{XY} = 1.1$.
• Calculate $r^2$: $r^2 = b_{YX} \times b_{XY} = 1.3 \times 1.1 = 1.43$.

Since $r^2$ cannot be greater than 1, Option 2 is false.

Option 3 Analysis (True Statement C)

Equations: $Y = 1 + 1.6X$ and $X = 3 + 0.5Y$.

• Regression coefficient of $Y$ on $X$: $b_{YX} = 1.6$.
• Regression coefficient of $X$ on $Y$: $b_{XY} = 0.5$.
• Calculate $r^2$: $r^2 = b_{YX} \times b_{XY} = 1.6 \times 0.5 = 0.8$.

Since $0 \le 0.8 \le 1$, this is a valid value for $r^2$. Option 3 is true.

Option 4 Analysis (True Statement D)

Equations: $Y = 1 + X$ and $X = Y$.

• Regression coefficient of $Y$ on $X$: $b_{YX} = 1$.
• Regression coefficient of $X$ on $Y$: $b_{XY} = 1$.
• Calculate $r^2$: $r^2 = b_{YX} \times b_{XY} = 1 \times 1 = 1$.

This implies $r = \pm 1$. The statement correctly notes that the correlation is $\pm 1$. This consistency makes Option 4 true.

Conclusion on True Statements

Based on the analysis, statements 3 and 4 are true.