The slope b and intercept a of a least squares line can be calculated from the means and standard deviations of the two variables, along with the correlation coefficient, as follows: b = r(s_y/s_x) and a = yÌ… ˆ’ bxÌ…. These summary statistics for the day hikes described in the previous two exercises are:

a. Use these statistics to determine the slope b and intercept a for predicting time from distance.
b. Use these statistics to determine the slope b and intercept a for predicting time from elevation gain.
c. Use the least squares line to predict the time needed for a hike with distance equal to the mean of the distances.
d. Use the least squares line to predict the time needed for a hike with elevation gain equal to the mean of the elevation gains.
e. What do you notice about your predictions in parts (c) and (d)?

Transcribed Image Text:

Correlation with time Mean SD 3.283 1.856 Distance 0.916 Elevation gain 333.2 355.5 0.344 Time 102.08 63.79 1.000