New data is added to change the mean time to 6 mninutes and 10 seconds with standared deviation 2 minutes and 5 seconds. The mean depth is now 115.5 feet with standard deviation 31.6 feet. If the association is still negative and r^2=.68, find the slope of the regression line of time versus depth.
To find the slope of the regression line of time versus depth, let's break down the steps:
1. Calculate the correlation coefficient (r) from the given r^2 value:
- Since r^2 = 0.68, the value of r can be found by taking the square root of 0.68.
- r = √(0.68) ≈ 0.8246
2. Determine the slope (b) of the regression line using the formula:
- b = r * (standard deviation of the dependent variable / standard deviation of the independent variable)
- In this case, the dependent variable is time (T) and the independent variable is depth (D).
3. Calculate the new standard deviation for time and depth:
- Since new data is added, we need to update the standard deviation values according to the given information.
- The new standard deviation for time is 2 minutes and 5 seconds.
- The new standard deviation for depth is 31.6 feet.
4. Substitute the values into the formula to find the slope:
- b = r * (standard deviation of T / standard deviation of D)
- b = 0.8246 * (2 min 5 sec / 31.6 ft)
5. Convert minutes and seconds to a single unit for time:
- 2 min 5 sec is equivalent to 2.0833 minutes (since 1 minute = 60 seconds).
6. Calculate the slope:
- b = 0.8246 * (2.0833 min / 31.6 ft)
- b ≈ 0.05436
Therefore, the slope of the regression line of time versus depth is approximately 0.05436.