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	175	1952	71	45	25	28	58	30

x	69	44	37	70	20	45	49
y	292	61	194	36	66	208	48

(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 =

Answer 1

We are given,

x	50	71	55	50	33	58	79	26
y	175	1952	71	45	25	28	58	30

x	69	44	37	70	20	45	49
y	292	61	194	36	66	208	48

From these values

Let the simple linear regression line be

Now,

Hence, the linear regression model is

When rock surface area, x= 70, then

given, when x= 70, y= 36

When rock surface area, x= 71, then

given, when x= 71, y= 1952

(b) The correlation coefficient is

Then, the coefficient of determination is

(c)   If we eliminate x= 71, y= 1952, then we have

Let the simple linear regression line be

Now,

Hence, the linear regression model is