# 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 ...

Statistics: Multiple Regression Analysis

41. A multiple regression analysis based on n= 24 data points yielded the following fitted model:

Y = 130.0093 - 3.5017 + .0034

The error sum of squares was 465.1348. Each of the following statements is incorrect; your job is to correct each.

a. For each one-unit change in , we expect Y to decrease by -3.5017 units

b. The estimated standard error of the regression is 22.1493

c. There is a direct relation between and Y

d. The fitting error for the data point Y = 50, , and = 1024 is 52.1565

e. If we reduce the value of from 0.0034 to 0.0014, the error sum of squares will

be less than 465.1348

42. Find the cutoff F-value for the following testing situations:

a. Ho: Beta 1 = Beta 2 = Beta 3 = 0; n = 28; and significance level = 0.05

b. Ho: Beta1 = Beta 2 = Beta 3 = Beta 4 = Beta 5 = Beta 6 = 0; n = 35; and significance level = 0.10

c. Ho: Beta 1 = Beta 2 = 0; n = 15; and significance level = 0.01

43, 44. See attached word document.

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