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. x50 71 55 50 33 58 79 26 y 161 1938 57 31 11 14 44 16 x 69 44 37 70 20 45 49 278 47 180 22 52 194 34 (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 residuals for both points are positive. O The residual for the first point is positive, while the residual for the second point is negative. The residual for the first point is negative, while the residual for the second point is positive. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) y = Interpret the coefficient of determination. O The coefficient f 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 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. 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. The coefficient of determination is the increase in colony density due to an increase in one unit of colony density. (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.)
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. x50 71 55 50 33 58 79 26 y 161 1938 57 31 11 14 44 16 x 69 44 37 70 20 45 49 278 47 180 22 52 194 34 (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 residuals for both points are positive. O The residual for the first point is positive, while the residual for the second point is negative. The residual for the first point is negative, while the residual for the second point is positive. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.) y = Interpret the coefficient of determination. O The coefficient f 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 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. 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. The coefficient of determination is the increase in colony density due to an increase in one unit of colony density. (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.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.CR: Chapter 1 Review
Problem 86CR
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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 161 1938 57 31 11 14 44 16
X 69 44 37 70 20 45 49
278 47 180 22 52 194 34
Y
(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 residuals for both points are positive.
O The residual for the first point is positive, while the residual for the second point is negative.
The residual for the first point is negative, while the residual for the second point is positive.
(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 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 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.
y =
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.
(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.)
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VIEWStep 3: Calculate the predicted value of the colony density when surface area is given.
VIEWStep 4: Calculated the coefficient of determination and interprets it.
VIEWStep 5: Determine the predicated regression equation when eliminating the second observation.
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