Question

the graph shows the best-fit regression model for a set of data comparing the number of hours spent hiking and the number of miles traveled in one day.

which is most likely true of the data set represented by the regression model on the graph?

each point in the data set falls on the regression line.
the regression model is an accurate representation of the distance for any number of hours hiked.
each point in the data set is near the regression line.
the regression model is inaccurate, as it does not begin at (0, 0).

Explanation:

Analyze the scatter plot and regression line

The graph displays five data points representing hours spent hiking versus distance traveled. A line of best fit with the equation \(y = 3.65x + 0.1\) is drawn through the data.

Evaluate the given statements

• Statement 1: "Each point in the data set falls on the regression line." Looking at the graph, the points at \(x = 1\) and \(x = 2\) do not lie exactly on the line. Thus, this statement is false.
• Statement 2: "The regression model is an accurate representation of the distance for any number of hours hiked." A linear model cannot accurately predict distance for any number of hours (e.g., extremely large values where physical limits apply). Thus, this statement is too absolute.
• Statement 3: "Each point in the data set is near the regression line." All five plotted data points lie extremely close to the drawn line of best fit, indicating a strong linear relationship. This is the most likely true statement.
• Statement 4: "The regression model is inaccurate, as it does not begin at (0, 0)." A regression model does not need to start at the origin to be accurate. Thus, this statement is false.

Determine the correct option

The third option is the most accurate and standard interpretation of a strong best-fit linear regression model.

Answer:

• Each point in the data set falls on the regression line.
• The regression model is an accurate representation of the distance for any number of hours hiked.
• Each point in the data set is near the regression line. (Correct answer)
• The regression model is inaccurate, as it does not begin at (0, 0).