The invasive diatom species Didymosphenia geminata has the potential to inflict

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.

(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:

(b) Calculate the coefficient of determination. (Round your answer to three decimal places.)

(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=

Explanation / Answer

Solution:

The regression equation is

y = - 281 + 9.96 x

Predictor        Coef     SE Coef          T        P

Constant       -280.9       390.2      -0.72    0.484

x               9.963       7.354       1.35    0.199

S = 472.4       R-Sq = 12.4%     R-Sq(adj) = 5.6%

Analysis of Variance

Source            DF          SS          MS         F        P

Regression         1      409534      409534      1.84    0.199

Residual Error    13     2900807      223139

Total             14     3310341

a)Before prediction we have to check correlation is valid or not.

Here r = correlation between x and y = 0.352 and p-value =0.199

Here p-value > (0.05) Hence accept H0.

That is x and y are not correlated.

Hence in this case we use mean of (y bar) as a prediction.

When x = 70 then y=221.27

And corresponding residual are 60.53

When x=71 then y = 221.7

And residuals = 58.350

b)Coefficeint of determination = 12.4%= 0.124

c) Neglecting second observation. Regression equation is.

y = 59.4 + 0.78 x

Done

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