Questions: b. Choose the correct choice below. A. The predictor is household size. The response is monthly water bill. Larger households tend to use more water. B. The predictor is monthly water bill. The response is household size. Larger water bills tend to result in smaller families. C. The predictor is household size. The response is monthly water bill. Larger households tend to use less water. D. The predictor is monthly water bill. The response is household size. Larger water bills tend to result in larger families.

Solution Steps

The mean of \( x \) (household size) is calculated as: \[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = \frac{1 + 2 + 3 + 4 + 5 + 6}{6} = 3.5 \]

The mean of \( y \) (monthly water bill) is calculated as: \[ \bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = \frac{30 + 45 + 60 + 75 + 90 + 105}{6} = 67.5 \]

The correlation coefficient \( r \) is given as: \[ r = 1.0 \]

The numerator for \( \beta \) is: \[ \sum_{i=1}^{n} x_i y_i - n \bar{x} \bar{y} = 1680 - 6 \cdot 3.5 \cdot 67.5 = 262.5 \]

The denominator for \( \beta \) is: \[ \sum_{i=1}^{n} x_i^2 - n \bar{x}^2 = 91 - 6 \cdot 3.5^2 = 17.5 \]

Thus, the slope \( \beta \) is: \[ \beta = \frac{262.5}{17.5} = 15.0 \]

The intercept \( \alpha \) is: \[ \alpha = \bar{y} - \beta \bar{x} = 67.5 - 15.0 \cdot 3.5 = 15.0 \]

The line of best fit is: \[ y = 15.0 + 15.0x \]

Given the positive correlation coefficient \( r = 1.0 \) and the positive slope \( \beta = 15.0 \), we can conclude that larger households tend to use more water.

Final Answer