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The invasive diatóm species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colónization 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 172 1949 68 42 22 25 55 27 69 44 37 70 20 45 49 y 289 58 191 33 63 205 45 (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 density corresponding residual How do the residuals compare? O The residuals for both points are negative. O The residual for the first point is positive, while the residual for the second point is negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive.

The invasive diatóm species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colónization 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 172 1949 68 42 22 25 55 27 69 44 37 70 20 45 49 y 289 58 191 33 63 205 45 (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 density corresponding residual How do the residuals compare? O The residuals for both points are negative. O The residual for the first point is positive, while the residual for the second point is negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive.

MATLAB: An Introduction with Applications
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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(b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determinațion. O The coefficient of determination is the increase in rock surface area due to an increase in one unit of rock surface area. O The coefficient of determination is the increase in colony density due to an increase in one unit of colony density. O The coefficient of determination is the proportion of the total variation in colony density that can be explained by a linear regression model with rock surface area as the predictor. O The coefficient of determination is the probability that the regression model fits the data. O The coefficient of determination is the proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. (c) The second observation has a very extreme y value (in the full data set consisting of 72 observations, there were two of these). This observation may have had a substantial impact on the fit of the model and subsequent conclusions. Eliminate it and recalculate the equation of the estimated regression line. (Round your values to three decimal places.) y = Does it appear to differ substantially from the equation before the deletion? O The new equation is substantially different. O The new equation is not substantially different. What is the impact on r2 and s? O r2 and are both smaller. O r2 and s are both larger. O r2 is smaller, while s is larger. Or is larger, while s is smaller.
Transcribed Image Text:(b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determinațion. O The coefficient of determination is the increase in rock surface area due to an increase in one unit of rock surface area. O The coefficient of determination is the increase in colony density due to an increase in one unit of colony density. O The coefficient of determination is the proportion of the total variation in colony density that can be explained by a linear regression model with rock surface area as the predictor. O The coefficient of determination is the probability that the regression model fits the data. O The coefficient of determination is the proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. (c) The second observation has a very extreme y value (in the full data set consisting of 72 observations, there were two of these). This observation may have had a substantial impact on the fit of the model and subsequent conclusions. Eliminate it and recalculate the equation of the estimated regression line. (Round your values to three decimal places.) y = Does it appear to differ substantially from the equation before the deletion? O The new equation is substantially different. O The new equation is not substantially different. What is the impact on r2 and s? O r2 and are both smaller. O r2 and s are both larger. O r2 is smaller, while s is larger. Or is larger, while s is smaller.
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. 50 71 55 50 33 58 79 26 y| 172 1949 68 42 22 25 55 27 69 44 37 70 20 45 49 y| 289 58 191 33 63 205 45 (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 density corresponding residual How do the residuals compare? O The residuals for both points are negative. O The residual for the first point is positive, while the residual for the second point is negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive.
Transcribed Image Text: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. 50 71 55 50 33 58 79 26 y| 172 1949 68 42 22 25 55 27 69 44 37 70 20 45 49 y| 289 58 191 33 63 205 45 (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 density corresponding residual How do the residuals compare? O The residuals for both points are negative. O The residual for the first point is positive, while the residual for the second point is negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive.
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