Question

effect of water on bean production
water applied daily in centimeters 0.5 1.0 1.5 2.0 2.5 3.0
beans produced in kilograms 1.6 1.8 2.0 2.4 2.6 2.8
graph: beans produced in kg (y-axis) vs water applied in cm (x-axis), with points at (0.5,1.6), (1.0,1.8), (1.5,2.0), (2.0,2.4), (2.5,2.6), (3.0,2.8)
using the table and graph showing the effect of water on bean production, select all of the statements below that are true.

• the data are approximately linear.
• the y-intercept of the trend line for the data is about 1.6 cm.
• adding more water seems to produce more beans.
• the trend line indicates that, even with no water applied, you can expect about 1.4 kg of beans to be produced.
• the data show a strong positive correlation.
• the data show a strong negative correlation.

Explanation:

1. "The data are approximately linear": The points in the graph and the table values show a roughly straight - line pattern. As water applied (x - value) increases, beans produced (y - value) increases in a way that is close to linear.
2. "The y - intercept of the trend line for the data is about 1.6 cm": The y - intercept is a value on the y - axis (beans produced in kg), not in cm. So this statement is incorrect.
3. "Adding more water seems to produce more beans": From the table, as water applied daily (0.5, 1.0, 1.5, 2.0, 2.5, 3.0 cm) increases, the beans produced (1.6, 1.8, 2.0, 2.4, 2.6, 2.8 kg) also increases. So this is true.
4. "The trend line indicates that, even with no water applied, you can expect about 1.4 kg of beans to be produced": We can find the equation of the trend line. Let's assume the linear equation is \(y = mx + b\). Using two points, say (0.5, 1.6) and (1.0, 1.8). The slope \(m=\frac{1.8 - 1.6}{1.0 - 0.5}=\frac{0.2}{0.5} = 0.4\). Then using point - slope form \(y - 1.6=0.4(x - 0.5)\), \(y=0.4x+1.6 - 0.2=0.4x + 1.4\). When \(x = 0\) (no water), \(y = 1.4\) kg. So this is true.
5. "The data show a strong positive correlation": Since as one variable (water applied) increases, the other variable (beans produced) increases, and the points are close to a straight line, there is a strong positive correlation.
6. "The data show a strong negative correlation": This is false because the variables are positively related, not negatively.

Answer:

• The data are approximately linear.
• Adding more water seems to produce more beans.
• The trend line indicates that, even with no water applied, you can expect about 1.4 kg of beans to be produced.
• The data show a strong positive correlation.