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 xrock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data. x 50 71 y 157 1934 53 27 7 55 50 33 58 79 26 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.) ya 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. The residuals for both points are positive. O The residuals for both points are 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. 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 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. The coefficient of determination is the probability that the regression model fits the data. 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? The new equation is substantially different. The new equation is not substantially different. What is the impact on 2 and s? Oands are both smaller. O2 is smaller, while s is larger. O2 and a are both larger. O 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 xrock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data. x 50 71 y 157 1934 53 27 7 55 50 33 58 79 26 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.) ya 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. The residuals for both points are positive. O The residuals for both points are 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. 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 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. The coefficient of determination is the probability that the regression model fits the data. 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? The new equation is substantially different. The new equation is not substantially different. What is the impact on 2 and s? Oands are both smaller. O2 is smaller, while s is larger. O2 and a are both larger. O is larger, while s is smaller.

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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Related questions

Question

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 density
corresponding residual

How do the residuals compare?

The residual for the first point is positive, while the residual for the second point is negative. The residuals for both points are positive. The residuals for both points are 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.

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. The coefficient of determination is the probability that the regression model fits the data. 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?

The new equation is substantially different. The new equation is not substantially different.

What is the impact on r² and s?