Question

Answer #1,3,4,5 thanks.

The data in table 1 are of peak 1. Make the following rver stage (gage height) and river discharge from 1916-1931 for Cumberland height) an River at Cumberland Falls, Kentucky separate graphs: 1. a scatterplot of the Water Year vs Gage Height, and 2. a Discharge. Note. Water Year should be placed on the x-axes. two scatterplot of Water Year vs River 3. 4. nd the mean, median, mode, and standard deviation for the gage heights and river Calculate the correlation coefficient between gage height Find the linear regression and river discharge. Interpret the result. predicting the river discharge from the gage height. Graph the linear ine What would be the river discharge if the gage height is 17.55 feet in 2016? e a comprehensive technical report using all the information calculated (include graphs). In your for the (nclude your thoughts of what the rainfall regime may have been during the 1916-1951 perio for the Cumberland River. Table 1. Peak Discharge for Cumberland River at Cumberlanod Falls, Kentucky (1916-1931) River Discharge Water Year 1916 Gage Height (feet) 12.90 13.20 15.50 11.40 12.60 9.80 11.70 10.30 11.00 10.30 9.20 14.10 10.40 14.90 8.80 9.50 (cubic feet/second) 45,200 47,000 59,600 37,200 43,500 28,200 38,600 30,900 35,100 30,900 25,600 Date Dec. 18 March 4 1917 1918 1919 1920 1921 1922 1923 1924 an an Jan 23 Apr 17 Feb 21 Feb 3 1925 1926 Feb 16 May 1 Dec 25 1927 1928 1929 1930 51,900 31,600 un 56,100 23,600 26,800 Mar 23 Nov 18 Apr

Answer 1

1)

a)

b)

3)

Correlation Coefficient is calculated using the given below formulae:

Hence, r = 0.9998

The value indicates very strong linear correlation between the two variables ie when one variable increases, the other also increases and vice versa.

4)

Regression Output

Regression Equation

River Discharge = 5,420.10 * Gage Height - 24,635.66

When Gage Height = 17.55,

River Discharge = 5,420.10 * 17.55 - 24,635.66 = 70,487.09 cubic feet/second.

5)

From scatterplot 1 we conclude that Gage Height decreased over time.

From scatterplot 2 we can also conclude that River Discharge decreased over time.

From Scatterplot 3, we can conclude that Gage Height and River Discharge are very strongly corelated.