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 actual hiking data and a solid line representing the linear regression model \(y = 3.65x + 0.1\).

• Not all points lie exactly on the line, which rules out the statement that every point falls on the regression line.
• The points are distributed very close to the line, indicating a strong linear correlation.

Evaluate the given statements

• "Each point in the data set falls on the regression line": Incorrect, as points like \((1, 2)\) and \((3, 12)\) lie slightly off the line.
• "The regression model is an accurate representation of the distance for any number of hours hiked": Incorrect, because extrapolation to "any" number of hours (e.g., 100 hours) is not guaranteed to be accurate.
• "Each point in the data set is near the regression line": Correct, as all plotted data points lie in close proximity to the line of best fit.
• "The regression model is inaccurate, as it does not begin at (0, 0)": Incorrect, a regression line does not need to pass through the origin to be accurate.

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).