The Quantitative Environmental Learning Project reports on a study of river velocity versus depth: The data "were acquired at a station below Grand Coulee Dam at a distance of 13 feet from the edge of the river. The depth of the Columbia River at this spot was about 12 feet at the time of measurement. Velocities were measured at various heights in the water column."15 Depths are recorded in feet and velocities in feet per second:
a. Use software to produce a scatterplot of the data, and choose the correct word in each pair to complete this quotation from the report: "These data show a regular (1) increase/decrease of velocity with increasing depth of the river, as might be expected. The data are fairly (2) linear/curved, with a (3) low/high correlation coefficient."
b. If depth were recorded in meters instead of feet, which would be different: the value of r, the equation of the regression line, both of these, or neither of these?
c. How many degrees of freedom are appropriate for the t statistic used to test if the population slope b1 of the regression line is zero?
d. Report the t statistic and the P-value for this test, and state a conclusion about whether or not depth and velocity are related in general.
e. Tell whether each of the following focuses on data production, displaying and summarizing data, probability, or statistical inference:
1. Finding slope b1 and standardized slope t for the data
2. Finding the P-value
3. Deciding whether or not depth and velocity are related in general
4. Arriving at a method to obtain water depths and velocities