# Biostatistics - Multiple Regression Analysis

See attached files. This is an exercise requiring multiple regression analysis to be used. Details of requirements are in "The task" section of attached Asst7 document.

Attached documents:

1. Asst7 = description and requirements

2. asst7.csv = dataset to be used for analysis

3. Lab manual.pdf = see Multiple Regression section starting on p. 129

Note: It is very important to use Multiple Regression analysis and other information from the Lab Manual - Multiple Regression section.

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#### Solution Preview

See attached files.

I've done the analyses in Excel (using the Regression function in the Analysis ToolPak). All results should be the same as if you did them in R.

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Analyze the data to assess the relative importance and the significance of these putative factors as determinants of black fly abundance. In your answer, you should provide:

1) An explicit statement of all null and alternate hypotheses (are they one or two-tailed?).

We are interested in determining which of the independent variables (below) influence the biomass of black flies. The dependent variable is bsim, the biomass of black fly larvae.

Independent variables:

1- distance, the distance in meter from the closest lake upstream of the sampling station

2- cs, an index of the nutritive quality of the particles suspended in the water column (it is the ratio of the concentration of chlorophyll a to the total concentration of particles (organic and inorganic))

3- v, the current velocity (in cm/s)

4- z, the water depth (in cm)

5- a, the average surface area of rocks (in cm2)

We will do multiple regression analysis. The null hypotheses are that the coefficients of each independent variable are equal to 0. The alternative hypotheses are that the coefficients of each independent variable are not equal to 0.

These hypotheses are two-tailed.

2) A rationale for your choice of statistical procedure(s) to test the null hypotheses specified in (1).

Because we are interested in determining the influence of several independent variables on the value of a dependent variable, multiple regression analysis is appropriate.

3) An explicit statement of the statistical conclusion and its biological interpretation.

I did the analyses in Excel.

When ...