A survey study of Biological stream has been conducted and the number of fish pe

Question

A survey study of Biological stream has been conducted and the number of fish per 75-meter section of stream has been counted. The following physical and chemical factors are also recorded (1) dissolved oxygen (mg/liter). (2) nitrate concentration (mg/liter); and (4) water temperature on the sample data (degrees) (a) Fit a full regression model, compute ALL partial regression coefficients and Y intercept What proportion of variation in fish abundance that can be explained by the linear regression of those physical and chemical characteristics? (b) Report the ANOVA table of this regression and test the hypothesis that there is no significant multiple regression relationship. (c) Are all these characteristics good predictors for the abundance of fish in a stream? Which one(s) you would like to keep in your future analysis, which one(s) you would like to remove? Provide the test result for each independent variable to support your conclusion.

Explanation / Answer

The regression equation is
Numfish = - 119 + 8.54 oxygen + 7.41 nitrogen + 5.92 sulfate - 0.07 temp

Predictor Coef SE Coef T P
Constant -119.49 44.31 -2.70 0.022
oxygen 8.539 2.901 2.94 0.015
nitrogen 7.409 4.933 1.50 0.164
sulfate 5.918 2.439 2.43 0.036
temp -0.069 1.226 -0.06 0.956

S = 23.6491 R-Sq = 75.9% R-Sq(adj) = 66.3%

So of the total variation in fish abundance only 75.9% explained by the regression equation/
Analysis of Variance

Source DF SS MS F P
Regression 4 17609.6 4402.4 7.87 0.004
Residual Error 10 5592.8 559.3
Total 14 23202.4

Here null hypothesis: the regression is significant

alternative:the regression is not significant.

as p value less than alpha=0.05

so at 5% level of sinificance in the light of the given data we reject Ho and conclude that the regression is not significant.

Predictor Coef SE Coef T P
Constant -119.49 44.31 -2.70 0.022
oxygen 8.539 2.901 2.94 0.015
nitrogen 7.409 4.933 1.50 0.164
sulfate 5.918 2.439 2.43 0.036
temp -0.069 1.226 -0.06 0.956

from the p values we can say the variables temparature and nitrogen can be dropped

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