Question

a landscaper applies weed killer to a lawn and records the area, in square feet, of the weeds each week since the weed killer was applied. after creating a scatter plot of the data, the landscaper draws two different linear models to represent the data. which statement is true? linear model 1 fits the data better than linear model 2 because linear model 1 is close to many data points. linear model 1 fits the data better than linear model 2 because linear model 1 is close to the highest data point. linear model 2 fits the data better than linear model 1 because linear model 2 intersects the x - axis. linear model 2 fits the data better than linear model 1 because linear model 2 is below all data points.

Explanation:

Step1: Understand the concept of a good - fitting linear model

A good - fitting linear model is one that is close to many data points. The closer the line of the linear model is to the majority of the data points, the better it represents the data.

Step2: Analyze each option

• Option 1:

If a linear model is close to many data points, it is a better fit. In Linear Model 1, the line is close to many data points.

• Option 2:

A model being close to the highest data point does not necessarily mean it is a good fit for all the data. A good fit should consider the overall distribution of data points, not just the highest one.

• Option 3:

Intersecting the \(x\) - axis has no relation to how well a linear model fits the data. The fit of a linear model is based on the proximity of the line to the data points, not on where it intersects the axes.

• Option 4:

A model being below all data points is not a characteristic of a good - fitting model. A good - fitting model should be among the data points, not below or above all of them.

Answer:

Linear Model 1 fits the data better than Linear Model 2 because Linear Model 1 is close to many data points.