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:

• For the first option: A regression line is a best - fit line, and not all data points fall exactly on it. So this is false.
• For the second option: A regression model is a model based on the given data and has a domain of applicability related to the data range. It can't be accurate for any number of hours (e.g., negative hours or extremely large hours outside the data context). So this is false.
• For the third option: A best - fit regression line is constructed such that the data points are close to the line. From the graph, we can see that the points are near the line \(y = 3.65x+0.1\). So this is true.
• For the fourth option: The fact that the regression line does not start at \((0,0)\) does not make it inaccurate. The regression line is based on the best fit of the data, and the y - intercept is determined by the data. So this is false.

Answer:

Each point in the data set is near the regression line.