Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location.x 4 12 14 17 23 30 40 52 55 67 72 79 96 112 127y 4 10 13 15 15 25 27 45 38 46 53 74 82 99 105Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff.O Ho: P₁0H₂: B₁ <0OH:₁0H₂: P₁ = 0O Ho: P₁ = 0Ha: P₁ #0The regression equation isrunoff-2.03+0.852 rainfallState the appropriate null and alternative hypotheses.O Ho: P₁ = 0Ha: P₁0P-value=|PredictorConstantrainfallCoef-2.0330.85188Stdev2.3510.03622t-ratio-0.8623.52s 5.191 R-sq 97.7% R-sq(adj) 97.58р0.4030.000Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)t= State the conclusion in the problem context. (Use a = 0.05.)O Reject H. There is a useful linear relationship between runoff and rainfall at the 0.05 level.O Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.O Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.O Fail to reject H. There is a useful linear relationship between runoff and rainfall at the 0.05 level.Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m² increase in rainfall volume. (Round your answers to three decimal places.)])m³

The question is about regressionGiven :No. of pairs of x and y ( n ) = 15Coefficient of rainfall (…

Answered: Consider the following data on x =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

You are given the following data, where X1 (final percentage in math class) and X2 (number of absences) are used to predict Y (standardized math test score in third grade): Y X1 X2 345 70 390 80 1 370 75 4 375 92 400 82 350 70 3 310 61 5 420 80 375 88 3 410 72 1 485 99 300 65 7 Determine the following multiple regression values. Report intercept and slopes for regression equation accurate to 3 decimal places: Intercept: a = Partial slope X1: bị = Partial slope X2: bz = Report sum of squares accurate to 3 decimal places: SSreg Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places): F-ratio = P-value = Report the variance of the residuals accurate to 3 decimal places: Sres = Report the results for the hypothesis test for the significance of the partial slope for final percentage in math class (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to…
The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data. x 50 71 55 50 33 58 79 26 y 157 1934 53 27 7 10 40 12 x 69 44 37 70 20 45 49 y 274 43 176 18 48 190 30 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) y = Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density corresponding residual Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony…
The ages (in years) of five men and their systolic pressures. (You can use technology) Age, x 16 25 39 45 49 Systolic blood pressure, y 109 122 143 132 199 a. calculate the correlation coefficient, r b. calculate the critical r c. Is there a significant linear relationship between x and y? d. find the equation of regression line e Interpret the slope and the y-intercept f. Predict the systolic blood pressure for a man who is 40 years old.
Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 4 12 14 20 23 30 40 47 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 46 38 46 53 75 82 99 104 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation isrunoff = -2.07 + 0.850 rainfall Predictor Coef Stdev t-ratio p Constant -2.067 2.412 -0.86 0.407 rainfall 0.85038 0.03708 22.93 0.000 s = 5.321 R-sq = 97.6% R-sq(adj) = 97.4% State the appropriate null and alternative hypotheses. H0: ?1 = 0 Ha: ?1 > 0 H0: ?1 = 0 Ha: ?1 ≠ 0 H0: ?1 = 0 Ha: ?1 < 0 H0: ?1 ≠ 0 Ha: ?1 = 0 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. (Use ? = 0.05.) Reject H0. There is a useful linear relationship…
9 students were surveyed to see what their age is and what their income level is. Find the equation of the line using linear regression. We want to predict their age using their income. age 18 24 38 22 19 35 28 19 27 income 456 786 835 855 645 244 587 1400 975 Just a side note, the 19 year old is making 1400, would be considered an outlier since they are making way more than everyone else. (y=-.0061x+34.9874 4 decimals) y=30.3709-.0064
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y (a) x= 150 calories (c) x= 120 calories (b) x= 90 calories (d) x=60 calories 160 180 130 130 80 190 415 465 350 380 270 540 (c) Predict the value of y for x= 120. Choose the correct answer below O A. 347 151 O B. 279.801 O C. 414.501 O D. not meaningful (d) Predict the value of y for x= 60. Choose the correct answer below. O A. 414.501 O B. 212.451 tes O C. 279.801
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 90% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $825. The equation of the regression line is y = 1.597x- 169.203. Wages (state), x Wages (federal), y 742 775 783 802 842 890 912 939 949 954 1,002 1,039 1,097 1,145 1,199 1,242 1,271 1,299 1,335 1,398 Construct and interpret a 90% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $825. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. There is a 90% chance that the predicted average weekly wages of federal government employees is between S and S given a state average weekly wage of $825. O B. We can be 90%…
In the graph shown below consider the horizontal line to represent the average y value for the data set and the slant line to represent the linear regression equation. use only the graph of the data to do the following:
The table shows a country's average fuel consumption for "light duty" vehicles (passenger cars and small trucks) for several years. Let x be the number of years since 1985, so that x = 5 stands for 1990 and so forth. Year Fuel Economy (mpg) 1990 16.9 1995 17.7 2000 18.3 (a) Find the linear regression model for these data. What does the slope in the regression model represent? 2005 18.9 (b) Use the linear regression model to predict the country's average fuel economy for light duty vehicles in the year 2035. 2010 19.6 (a) Find the linear regression model for these data. Choose the correct answer below. (Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS