### Linear Regression Analysis: Rainfall and Runoff Volume#### OverviewAn article analyzed the relationship between rainfall volume ($x$) and runoff volume ($y$) using a scatter plot with a least squares regression line for a specific location. The data recorded is as follows:- $x$ (Rainfall volume in $m^3$): 7, 12, 14, 17, 23, 30, 40, 47, 55, 67, 72, 84, 96, 112, 127- $y$ (Runoff volume in $m^3$): 4, 10, 13, 14, 15, 27, 35, 40, 46, 53, 71, 82, 99, 104#### Analysis**(a) Support for Simple Linear Regression Model**The scatter plot of data verifies a reasonable linear relationship, supporting the use of the simple linear regression model.**(b) Estimates for Slope and Intercept**The point estimates for the regression line's slope and intercept are:- **Slope**: 0.8444- **Intercept**: -2.3161**(c) Estimation of Average Runoff Volume**Given a rainfall volume of 46 $m^3$, the estimated average runoff volume is 36.5263 $m^3$.**(d) Standard Deviation Estimate**The standard deviation estimate was not calculated in this analysis.**(e) Proportion of Variation Explained**The worksheet provides a section to input the proportion of observed variance in runoff volume attributable to the regression relationship between rainfall and runoff. The answer should be rounded to four decimal places.### ConclusionThis analysis demonstrates the application of linear regression to predict runoff volume based on rainfall data, aiding in understanding the dynamics between these two environmental factors.

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Answered: particular location. The accompanying…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 11 9 12 8 11 13 4 13 6. 6 У 7.25 7 12.94 7.22 8.15 9.27 6.33 5.3 8.52 6.14 5.46 Create a scatterplot of the data. Choose the correct graph below. O B. OC. O D. O A. Ay 25- Ay 25- 25- 25- 20- 20 20- 20 15 15 15 15 10 10 10- 10 5- 5- 5- 5- 0- 05 10 15 20 25 05 10 15 20 25 0- 05 10 15 20 25 0 5 10 15 20 25 Find the equation of the regression line. (Round the constant two decimal places as needed. Round the coefficient to three decimal places as needed.) Identify a characteristic of the data that is ignored by the regression line. O A. There is no trend in the data. O B. The data has a pattern that is not a straight line. C. There is an influential point that strongly affects the graph of the regression line. D. There is no characteristic of the data that is ignored by the regression line. Click to select your answer(s).…
Height, x 772 628 518 508 496 483 stories, y 51 48 44 43 37 35 Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. (a) x = 498 feet (b) x = 640 feet (c) x = 345 feet (d) 735 feet Find the regression equation.Now construct a scatter plot of the data and draw the regression line. (a) Now use the regression equation to predict the value of y for each of the given x-values, if meaningful. Because the correlation between x and y is significant, the equation of the regression line can be used to predict y-values. However, prediction values are meaningful only for x-values in the range of the data. Begin with x = 498. Since x = 498…
Compute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and y-intercept to at least four decimal places. 43 37 15 19 24 37 18 y 72 67 25 29 42 65 32 Send data to Excel Regression line equation: y = 1.7777x + 1.5838
d the linear regression equation and the value of the linear correlation coefficient r. Round to 2 decimals. 19) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands): Cost| 7 2 3 4 2 5 9 10 Number 85 52 55 68 67 80 83 73 to Cost r =
The residual plot for a linear regression model is shown below. Assess the fit of the linear model, and justify your answer. The line is a good fit because the points on the residual plot have a clear pattern. The line is a good fit because the points on the residual plot do not have any noticeable pattern. The line is not a good fit because the points on the residual plot do not have any noticeable pattern. The line is not a good fit because the points on the residual plot have a clear pattern.
Complete parts (a) through (h) for the data below. 30 40 50 60 70 y 90 87 82 74 Question Help v 62 (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below. O A. OB. Ay 80- OC. Ay 80- OD. Av 20- 20 20 80 100 (d) By hand, determine the least-squares regression line. /Dound to throo donimal lncon an nondod Click to select your answer(s). M acer 9 esc # 2$ 6. 4 3 e W k h
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The following table shows students’ number of absences, x, and the student’s final grade,, y.# of absences x 6 2 15 9 12 5 8 Final grade y 82 86 43 74 58 90 78a) Calculate r, the correlation coefficient ________________b) Find the equation of the regression line __________________________________c) If a student is absent 4 times,, what grade does your regression line predict?__________________
The personnel director of a large hospital is interested in determining the relationship (if any) between an employee's age and the number of sick days the employee takes per year. The director randomly selects ten employees and records their age and the number of sick days which they took in the previous year. Employee 1 2 3 4 5 6 7 8 Age 30 50 40 55 30 28 60 25 Sick Days 7 4 3 2 9 10 0 8 Copy Data The estimated regression line and the standard error are given. Sick Days = 14.310162 - 0.2369(Age 9 10 30 45 5 2 Se = 1.682207 Find the 95% confidence interval for the average number of sick days an employee will take per year, given the employee is 26. Round your answer to two decimal places.
Here is data with y as the response variable. a. Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x,y). (x, y) b. Find the regression equation for the data set without the outlier. Enter the equation of the form mx + b rounded three decimal places. y wo X 48.4 77.3 88 67.1 108.3 75.9 64.8 -161.3 61.2 67.9 ŷw y 45.7 40.3 27.3 54.5 -63.2 36.3 73.2 96.5 82.2 119.8 = -- c. Find the regression equation for the data set with the outlier. Enter the equation of the form mx + b rounded to three decimal places.
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X	Y
7	4
12	10
14	13
17	14
23	15
30	25
40	27
47	45
55	38
67	46
72	53
84	71
96	82
112	99
127	104

X	Y
7	4
12	10
14	13
17	14
23	15
30	25
40	27
47	45
55	38
67	46
72	53
84	71
96	82
112	99
127	104

X	Y
7	4
12	10
14	13
17	14
23	15
30	25
40	27
47	45
55	38
67	46
72	53
84	71
96	82
112	99
127	104