The percentage of damage is thought to be a function of speed. In 15 different vehicles, theobservationsbetween speed and damage percentage were made, which can be seen in the table below.SpeedDamage Percentage85508035562862302138228115251074305019391894361004532941Assuming a linear relationship between velocity and percentage of damage E(Y\x) = a + ßx.calculate the regression coefficients. (Calculate by hand and get the result with at least fourdecimal places)a) Calculate the determination coefficient and the corrected determination coefficient of regression.(Calculate by hand and get the result with at least four decimal places)b) Plot the distribution between the velocity and the percentage of damage and add the regressionline to this graph. Plot this chart with Excel and add the equation of determination coefficient andregression line from the options on the chart so that you can compare the valuesthat you calculated in options a and b with these values.and R²c) Obtain 95% confidence intervals of regression coefficients. (Calculate manually and get the resultwith at least four decimal places.) please)d) Test the significance of the regression. The zero hypothesis should be that the slope is zero. Writedown the alternative hypothesis and the result of the test along with the istatistic interpretation.(Calculate by hand and get the result with at least four decimal places)e) Repeat the regression with R and compare the results obtained above. Add the output with R codeto your answer as a screenshot

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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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The percentage of damage is thought to be a function of speed. In 15 different vehicles, theobservations between speed and damage percentage were made, which can be seen in the table below.