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50 71 55 50 33 58 79 26 y 168 1945 64 38 18 21 51 23 69 44 37 70 20 45 49 y 285 54 187 29 59 201 41 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) 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 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. The residuals for both points are positive. O The residuals for both points are negative. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determination. O The coefficient of determination is the probability that the regression model fits the data. 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 proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. 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 increase in colony density due to an increase in one unit of colony density

50 71 55 50 33 58 79 26 y 168 1945 64 38 18 21 51 23 69 44 37 70 20 45 49 y 285 54 187 29 59 201 41 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) 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 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. The residuals for both points are positive. O The residuals for both points are negative. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determination. O The coefficient of determination is the probability that the regression model fits the data. 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 proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. 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 increase in colony density due to an increase in one unit of colony density

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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(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 r and s? O r2 and s are both larger. O r2 and s are both smaller. O r2 is smaller, while s is larger. O 2 is larger, while s is smaller.
Transcribed Image Text:(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 r and s? O r2 and s are both larger. O r2 and s are both smaller. O r2 is smaller, while s is larger. O 2 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 168 1945 64 38 18 21 51 23 x 69 44 37 70 20 45 49 y 285 54 187 29 59 201 41 (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 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. O The residuals for both points are negative. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determination. O The coefficient of determination is the probability that the regression model fits the data. 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 proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. 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 increase in colony density due to an increase in one unit of colony density.
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 168 1945 64 38 18 21 51 23 x 69 44 37 70 20 45 49 y 285 54 187 29 59 201 41 (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 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. O The residuals for both points are negative. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) Interpret the coefficient of determination. O The coefficient of determination is the probability that the regression model fits the data. 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 proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor. 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 increase in colony density due to an increase in one unit of colony density.
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