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	164	1941	60	34	14	17	47	19

x	69	44	37	70	20	45	49
y	281	50	183	25	55	197	37

(a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.)

y =

(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 =

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

Answer 1

using excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.351729174
R Square	0.123713412
Adjusted R Square	0.056306751
Standard Error	472.3759392
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	409533.5707	409533.5707	1.835329187	0.198576073
Residual	13	2900807.363	223139.0279
Total	14	3310340.933
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-293.8813264	390.2103963	-0.753135563	0.464789837	-1136.879636	549.1169833
x	9.96325383	7.354348555	1.354743218	0.198576073	-5.924850278	25.85135794

(a) the simple linear regression model to this data

y =-293.881+9.963 x

(b) the coefficient of determination is 0.124

(c) sfter eliminating

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.154383
R Square	0.023834
Adjusted R Square	-0.05751
Standard Error	87.22218
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2228.989	2228.989	0.292991	0.598216
Residual	12	91292.51	7607.709
Total	13	93521.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	46.37336	74.1943	0.625026	0.543657	-115.282	208.0289
x	0.779231	1.439591	0.541286	0.598216	-2.35737	3.915829

y = 46.373 +0.779 x

Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.)

colony density	46.373 +0.779 *70 =100.90~101
corresponding residual	25-101 = -76

Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.

colony density	46.373 +0.779 *71 =101.68~102
corresponding residual	1941-102 = 1839